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Superficies
mínimas, A. Ros, aparecerá en Florentino García Santos: In Memoriam,
Universidad de Granada, pdf. |
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The local removable
singularity theorem for minimal laminations, William H. Meeks III, Joaquín Pérez & Antonio
Ros, pdf. |
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In this paper we prove a local removable singularity theorem for certain minimal
laminations with isolated singularities in a Riemannian three-manifold. Then we show that a complete embedded
minimal surface in R3 with quadratic decay of curvature has finite total curvature |
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Stable constant mean curvature surfaces are area minimizing in small
L^1 neighborhoods, Frank Morgan
and Antonio Ros, Interfaces and Free
Boundaries 12 (2010), 151-155,
pdf. |
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We prove that a strictly stable
constant-mean-curvature surface in a smooth manifold of dimension less than
or equal to 7 is uniquely homologically area minimizing for fixed volume in a
small L^1 neighborhood. |
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Properly embedded surfaces with constant mean curvature, Antonio Ros and Harold Rosenberg, American Journal of Mathematics, 132 (2010), 1429-1443,
pdf. |
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We study some global
properties of surfaces with nonzero constant mean curvature in the Euclidean
3-space. We show that given two surfaces of this type, one of them
cannot stay at the convex side of the other. If the surface is symmetric
and lies in a narrow slab we prove that shape of the surface is similar
to the one of Lawson double periodic examples. |
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Limit leaves of
a cmc lamination are stable, William H. Meeks III, Joaquín Pérez and Antonio Ros, Journal of
Differential Geometry
84 (2010), 179-189, pdf |
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Stability of minimal and constant mean curvature surfaces with free
boundary, Matemática Contemporânea 35 (2009), 221-240, pdf. |
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We prove that stable balance minimal surfaces with free boundary in a
centrally symmetric mean-convex region of R^3 are topological
disks. For surfaces with constant mean curvature and free boundary, we prove
that volume-preserving stability implies that the surface has either genus
zero with at most four boundary components or genus one with 1 or 2 curves at
its boundary. This paper is dedicated
to Manfredo do Carmo on
his 80th Birthday |
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Properly
embedded minimal planar domains,
William H. Meeks III, Joaquín Pérez
and Antonio Ros, pdf |
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The only properly embedded minimal surfaces in the euclidean 3-space are the plane, the helicoid,
the catenoid and the Riemann minimal examples |
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Stable
constant mean curvature surfaces, William H. Meeks III, Joaquín
Pérez and Antonio Ros, in Handbook of
Geometric Analysis nº 1 (2008) 301-380. Editors: Lizhen
Ji, Peter Li, Richard Schoen, Leon Simon.
International Press. pdf |
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Stable periodic constant mean curvature
surfaces and mesoscopic phase separation. Interfaces and
Free Boundaries Volume 9, Issue 3
(2007), 355–365. pdf |
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We give a comprehensive description of the stable
solutions of the periodic isoperimetric problem in the case of lattice
symmetry. This result is intended to elucidate the geometry of certain
sophisticated interfaces appearing in mesoscale
phase separation phenomena. |
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Properly Embedded Minimal Surfaces with
Finite Topology, Proceedings of the International Congress
of Mathematics (Madrid 2006), Volume II, |
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We present a synthesis of
the situation as it now stands about the various moduli
spaces of properly embedded minimal surfaces of finite topology in flat
3-manifolds. This family includes the case of minimal surfaces with finite
total curvature in R3 as well as singly, doubly and triply
periodic minimal surfaces. |
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Liouville type
properties for embedded minimal surfaces, with William H.
Meeks III and Joaquín Pérez.
Communications in Analysis and Geometry 14 (2006),
703-723. pdf |
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We prove that a positive harmonic function on a
periodic minimal surface must be constant. |
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One-sided
complete stable minimal surfaces, J. Diff. Geom, 74
(2006), 69-92. pdf
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We prove that there are not complete one-sided
stable minimal surfaces in the euclidean 3-space.
We classify least area surfaces in the quotient of R^3 by one or two
linearly independent translations and we give sharp upper bounds of the genus
of compact two-sided index one minimal surfaces in non-negatively curved
ambient spaces. |
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The Geometry of
minimal surfaces of finite genus I: curvature estimates and quasiperiodicity, with William H. Meeks III and Joaquín
Pérez, J. Diff. Geom. 66 (2004), 1-45. pdf . |
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We prove curvature estimates for a sequence of properly embedded
minimal surfaces of finite genus and two limit ends, in terms of the
horizontal part of their normalized fluxes. |
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The Geometry of
minimal surfaces of finite genus II: nonexistente
of one limit end examples, with
William H. Meeks III and Joaquín Pérez, Invent. Math. 158 (2004). 323 - 341. pdf. |
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Isoperimetric inequalities in crystallography, J. Amer. Math. Soc. 17 (2004), 373-388. |
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We prove
sharp isoperimetric inequalities for regions which are invariant under a
given cubic space group, more... |
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The periodic isoperimetric problem, with L. Hauswirth, J. Perez and P. Romon,
Transactions of the AMS
356 (2004), no. 5, 2025--2047 |
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Given a
discrete group G of isometries in the 3-space, we
study among G-invariant regions with prescribed volume fraction, those whose
boundary has least area, more... |
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The Gauss map of minimal surfaces, Differential
Geometry, Valencia 2001, Proceedings of the conference in honour
of Antonio M. Naveira, O. Gil-Medrano and V. Miquel ed., World Scientific, (2002) 235-252, pdf. |
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We study
in a unified way several properties of the Gauss map of a minimal surface in
the Euclidean 3-space. In particular we consider stable minimal surfaces and
minimal surfaces whose Gauss map image omits certain points of the
sphere. The paper contains also an insight into the classical little and
great Picard theorems in one complex variable. |
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The
isoperimetric problem, Lecture series at the Clay Mathematics
Institute Summer School on the Global Theory of Minimal Surfaces, summer 2001, Mathematical Sciences Research Institute, Berkeley,
California, more... |
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Some
updates on isoperimetric problems, with M. Ritore, Mathematical
Intelligencer, 24 (2002) 9-14, pdf. |
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Proof of the double bubble conjecture, with M. Hutchings, F. Morgan and M. Ritoré, Ann.
of Math. 155 (2002), 459-489. |
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The standard double bubble minimizes
area among all compact surfaces in the Euclidean 3-space which enclose and
separate two regions of prescribed volumes, pdf |
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Minimal immersions of surfaces by
the first eigenfunctions and conformal area, with S. Montiel, Invent. Math. 83
(1986) 153-166. |
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Complete minimal surfaces with
index one and stable constant mean curvature surfaces, with F. J. López, Comment. Math. Helvet. 64 (1989) 34-43. |
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On embedded complete minimal
surfaces of genus zero, with F. J. López, J. Diff. Geom.
33 (1991) 293-300. |
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Schrodinger operators
associated with a holomorphic map, with S. Montiel, Proceedings conference on
global anal. and global diff. geom. At Berlin, 1990. Lecture notes in Math, 1481, Springer Verlag (1991) 147-174, pdf. |
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The Gauss map of minimal surfaces, Differential
Geometry, Valencia 2001, Proceedings of the conference in honour
of Antonio M. Naveira, O. Gil-Medrano and V. Miquel ed., World Scientific, (2002) 235-252, pdf. |
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Some uniqueness and nonexistence theorems for
Embedded minimal surfaces, with J. Pérez, Math. Ann. 295 (1993) 513-525, pdf. |
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Compactness of spaces of properly
embedded minimal surfaces with finite total curvature, Indiana Univ. Math. J. 44 (1995) 139-152. |
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Given a
sequence of minimal surfaces properly embedded in the euclidean 3-space which have genus one and r finite
total curvature ends, r > 4, there exists a subsequence
which converge (with multiplicity one) to a properly embedded minimal surface
with the same topology. |
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A two-piece property for compact
minimal surfaces in a three-sphere, Indiana Univ.
Math. J. 44 (1995) 841-849. |
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Embedded minimal surfaces : forces, topology and symmetries, Calculus of variations
and PDE, 4 (1996) 469-496. |
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The space of properly
embedded minimal surfaces with finite total curvature, with J. Pérez, Indiana Univ. Math.
J. 45 (1996) 177-204, pdf. |
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Uniqueness of the
Riemann minimal examples, with W. Meeks III and J. Pérez, Invent. Math. 131
(1998) 107-132. pdf |
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The space of complete
minimal surfaces with finite total curvature as lagrangian submanifold, with J. Pérez, Trans. A.M.S.
351 (1999) 3935-3952, pdf. |
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A Plateau problem at
infinity for properly immersed minimal surfaces with finite total curvature, with C. Cosín, Indiana Univ. Math. J. 50 (2001), 847-878. |
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We
construct properly immersed minimal surfaces in Euclidean 3-space with
prescribed asymptotic behaviour. more... |
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Properly embedded minimal
surfaces with finite total curvature, with J. Pérez, Lecture series at the CIME
course The Global Theory of Minimal Surfaces in Flat spaces at |
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Properly Embedded Minimal Annuli Bounded by a Convex Curve, with J. Pérez, Journal de l'Institut
Mathématique de Jussieu, 1
(2002) 293-305, pdf. |
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The Geometry of
minimal surfaces of finite genus I: curvature estimates and quasiperiodicity, with William H. Meeks III and Joaquín
Pérez, J. Diff. Geom. 66 (2004), 1-45. pdf . |
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The Geometry of
minimal surfaces of finite genus II: nonexistente
of one limit end examples, with
William H. Meeks III and Joaquín Pérez, Invent. Math. 158 (2004). 323 - 341. pdf. |
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One-sided
complete stable minimal surfaces,
J. Diff. Geom, 74 (2006), 69-92.
pdf |
|
We prove that there are not complete one-sided
stable minimal surfaces in the euclidean 3-space.
We classify least area surfaces in the quotient of R^3 by one or two
linearly independent translations and we give sharp upper bounds of the genus
of compact two-sided index one minimal surfaces in non-negatively curved
ambient spaces. |
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|
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Complete minimal surfaces with
index one and stable constant mean curvature surfaces,
with
F. J. López, Comment. Math. Helvet. 64 (1989)
34-43. |
|
|
|
Schrodinger operators associated with a holomorphic
map, with S. Montiel,
Proceedings conference on global anal. and global diff. geom. At Berlin, 1990. Lecture notes in Math, 1481, Springer Verlag (1991) 147-174,
pdf. |
|
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Stable constant mean curvature tori and the
isoperimetric problem in three-space forms,
with
M. Ritoré, .
Comment. Math. Helvet. 67 (1992) 293-305, pdf. |
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Stability for hypersurfaces
of constant mean curvature with free boundary,
with
E. Vergasta, . Geometriae dedicata 56 (1995)
19-33. pdf. |
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The spaces of index one minimal surfaces and stable
constant mean curvature surfaces embedded in flat three manifolds, with M. Ritoré ,Trans. A.M.S.
348 (1996) 391-410, pdf. |
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On stability of capillary surfaces
in a ball, with R. Souam,
Pacific Math. J. 178 (1997) 345-361. |
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Compact minimal hypersurfaces with index one in the real projective
space, with M. do Carmo and M. Ritoré, Comment. Math.Helvet. 75 (2000) 247-254, pdf. |
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The only
(two-sided) compact minimal hypersurfaces in the
real projective space whose Jacobi operator has index one are the minimal hyperquadrics. |
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Proof of the double bubble conjecture, with M. Hutchings, F. Morgan and M. Ritoré, Electron. Res. Announc. Amer.
Math. Soc. 6 (2000) 45-49. |
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The isoperimetric and Willmore
problems, Global Differential Geometry: the mathematical
legacy of Alfred Gray, M. Fernandez
& J. A: Wolf ed., Contemporay Mathematics 288 (2001) 149-161, pdf. |
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Lecture
given by the author at the International Congress on Differential Geometry, in memory of
Alfred Gray, September, 2000, |
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Proof of the double bubble conjecture, with M. Hutchings, F. Morgan and M. Ritoré, Ann. of Math. 155 (2002), no.
2, 459-489. |
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|
The
isoperimetric problem, Lecture series at the Clay Mathematics
Institute Summer School on the Global Theory of Minimal Surfaces, summer 2001, Mathematical Sciences Research Institute, Berkeley,
California, more... |
|
|
|
Some
updates on isoperimetric problems, with M. Ritore, Mathematical
Intelligencer (to appear) pdf. |
|
|
|
The periodic isoperimetric problem. with L. Hauswirth, J. Perez and P. Romon,
Transactions of the AMS
356 (2004), no. 5, 2025--2047, pdf. |
|
Given a discrete group G of isometries in
the 3-space, we study among G-invariant regions with prescribed volume
fraction, those whose boundary has least area, more... |
|
|
|
Isoperimetric inequalities in crystallography, J. Amer. Math. Soc. 17 (2004), 373-388. |
|
We prove
sharp isoperimetric inequalities for regions which are invariant under
a given cubic space group. more... |
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Compact hypersurfaces
with constant scalar curvature and a congruence theorem,
J.
Diff. Geom. 27 (1988) 215-220. |
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Compact hypersurfaces
with constant higher order mean curvatures, Revista
Mat. Iberoamer. 3 (1987) 447-453. |
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The Alexandrov
theorem for higher order mean curvatures, with S. Montiel, Proceedings conference in honour
of Manfredo do Carmo,
Pitman survey in pure and. appl. math . 52 (1991) 280-296. |
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Constant mean curvature surfaces in a halfspace of R3 with boundary in the boundary
of the halfspace,
with
H. Rosenberg, J. Diff. Geom. 44
(1996) 807-817, pdf. |
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Lagrangian submanifolds of C^n
with conformal Maslov form and the Withney sphere, with F. Urbano, J. Math. Soc. Japan
(1998) 203-226, pdf. |
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Properly embedded surfaces with constant mean
curvature, with H. Rosenberg, pdf. |
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Bending energy and Willmore conjecture |
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Minimal immersions of surfaces by
the first eigenfunctions and conformal area,
with
S. Montiel, Invent.
Math. 83 (1986) 153-166. |
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The Willmore conjecture in the
real projective space, Math. Research Letters 6 (1999)
487-494, pdf. |
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Any
antipodal invariant torus in the unit three sphere has total squared mean
curvature bigger than or equal to the one of the minimal Clifford torus. |
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The isoperimetric and Willmore problems, Lecture given
by the author at the International Congress on Differential Geometry, in memory of
Alfred Gray, September, 2000, |
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We review some of the methods used to study the isoperimetric problem
in 3-dimensional Riemannian manifolds. We also give a new result about the
topology of the isoperimetric regions in the positive curvature case and we
prove the Willmore conjecture for tori in Euclidean 3-space which are symmetric with
respect to a point. |
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