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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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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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