Profiles
Books
Antonio Alarcón, Franc Forstnerič, and Francisco J. López
Springer Monographs in Mathematics
Springer, Cham, 2021, xiv+428 pp.
ISBN: 978-3-030-69055-7 (print); 978-3-030-69056-4 (online)
Preprints
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Families of proper minimal surfaces
Antonio Alarcón and Franc Forstnerič
Preprint, 2026.
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Removing singularities of minimal surfaces by isotopies
Antonio Alarcón and Franc Forstnerič
Preprint, 2025.
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Generic properties of minimal surfaces
Antonio Alarcón and Francisco J. López
Proc. Roy. Soc. Edinburgh Sect. A, in press.
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The Mittag-Leffler theorem for proper minimal surfaces and directed meromorphic curves
Antonio Alarcón and Tjaša Vrhovnik
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), in press.
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Complete minimal surfaces with Cantor ends in minimally convex domains
Antonio Alarcón
Pure Appl. Funct. Anal., in press. (Issue dedicated to Nikolai Nadirashvili.)
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Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$
Antonio Alarcón and Francisco J. López
J. Eur. Math. Soc. (JEMS), in press.
Papers 2020-Today
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Isotopies of complete minimal surfaces of finite total curvature
Antonio Alarcón, Franc Forstnerič, and Finnur Lárusson
J. Lond. Math. Soc. 114 (2026), no. 1, Paper No. e70640.
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Holomorphic null curves in the special linear group
Antonio Alarcón and Jorge Hidalgo
Trans. Amer. Math. Soc. 379 (2026), no. 6, 4089-4119.
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On the Gauss map assignment for minimal surfaces and the Osserman curvature estimate
Antonio Alarcón and Francisco J. López
Ann. Mat. Pura Appl. 205 (2026), no. 2, 941-963.
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Oka-1 manifolds
Antonio Alarcón and Franc Forstnerič
Math. Z. 311 (2025), no. 2, Paper No. 33.
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Regular immersions directed by algebraically elliptic cones
Antonio Alarcón and Finnur Lárusson
J. Reine Angew. Math. (Crelle's J.) 823 (2025), 113-135.
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A strong parametric h-principle for complete minimal surfaces
Antonio Alarcón and Finnur Lárusson
J. Geom. Anal. 35 (2025), no. 2, Paper No. 42.
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Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure
Antonio Alarcón, Ildefonso Castro-Infantes, and Jorge Hidalgo
Commun. Contemp. Math. 27 (2025), no. 1, Paper No. 2450011.
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Hipersuperficies complejas completas en la bola de $\mathbb{C}^n$
Antonio Alarcón
Gac. R. Soc. Mat. Esp. 27 (2024), no. 3, 477-496. (Research-expository article, in Spanish.)
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Embedded complex curves in the affine plane
Antonio Alarcón and Franc Forstnerič
Ann. Mat. Pura Appl. 203 (2024), no. 4, 1673-1701.
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The space of Gauss maps of complete minimal surfaces
Antonio Alarcón and Finnur Lárusson
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 25 (2024), no. 2, 669-688.
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Complete nonsingular holomorphic foliations on Stein manifolds
Antonio Alarcón and Franc Forstnerič
Mediterr. J. Math. 21 (2024), no. 1, 25.
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The Yang problem for complete bounded complex submanifolds: a survey
Antonio Alarcón
In: Herrero, H., Navarro, M.C., Serrano, H. (eds) Cutting-Edge Mathematics. RSME 2022, RSME Springer Series 13 (2024), 1-25. Springer, Cham. (Research-expository article.)
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Wild holomorphic foliations of the ball
Antonio Alarcón
Indiana Univ. Math. J. 71 (2022), no. 2, 561-578.
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Algebraic approximation and the Mittag-Leffler theorem for minimal surfaces
Antonio Alarcón and Francisco J. López
Anal. PDE 15 (2022), no. 3, 859-890.
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Complete complex hypersurfaces in the ball come in foliations
Antonio Alarcón
J. Differential Geom. 121 (2022), no. 1, 1-29.
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Holomorphic Legendrian curves in $\mathbb{CP}^3$ and superminimal surfaces in $\mathbb{S}^4$
Antonio Alarcón, Franc Forstnerič, and Finnur Lárusson
Geom. Topol. 25 (2021), no. 7, 3507-3553.
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The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends
Antonio Alarcón and Franc Forstnerič
Rev. Mat. Iberoam. 37 (2021), no. 4, 1399-1412.
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A foliation of the ball by complete holomorphic discs
Antonio Alarcón and Franc Forstnerič
Math. Z. 296 (2020), no. 1-2, 169-174.
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Complex curves in pseudoconvex Runge domains containing discrete subsets
Antonio Alarcón
J. Anal. Math. 140 (2020), no. 1, 207-226.
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New complex analytic methods in the study of non-orientable minimal surfaces in $\mathbb{R}^n$
Antonio Alarcón, Franc Forstnerič, and Francisco J. López
Mem. Amer. Math. Soc. 264 (2020), no. 1283, vi+77 pp. Providence, RI: American Mathematical Society (AMS).
ISBN: 978-1-4704-4161-6 (print); 978-1-4704-5812-6 (online).
Papers 2006-2019
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Every meromorphic function is the Gauss map of a conformal minimal surface
Antonio Alarcón, Franc Forstnerič, and Francisco J. López
J. Geom. Anal. 29 (2019), no. 4, 3011-3038.
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A construction of complete complex hypersurfaces in the ball with control on the topology
Antonio Alarcón, Josip Globevnik, and Francisco J. López
J. Reine Angew. Math. (Crelle's J.) 751 (2019), 289-308.
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New complex analytic methods in the theory of minimal surfaces: a survey
Antonio Alarcón and Franc Forstnerič
J. Aust. Math. Soc. 106 (2019), no. 3, 287-341. (Research-expository article.)
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Darboux charts around holomorphic Legendrian curves and applications
Antonio Alarcón and Franc Forstnerič
Int. Math. Res. Not. IMRN 2019 (2019), no. 3, 893-922.
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Interpolation and optimal hitting for complete minimal surfaces with finite total curvature
Antonio Alarcón, Ildefonso Castro-Infantes, and Francisco J. López
Calc. Var. Partial Differential Equations 58 (2019), no. 1, 58:21.
Journal article • Full text view only • arXiv • Correction (Calc. Var. PDE 59 (2020), no. 5, 59:178, Open access link) -
Interpolation by conformal minimal surfaces and directed holomorphic curves
Antonio Alarcón and Ildefonso Castro-Infantes
Anal. PDE 12 (2019), no. 2, 561-604.
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Minimal surfaces in minimally convex domains
Antonio Alarcón, Barbara Drinovec Drnovšek, Franc Forstnerič, and Francisco J. López
Trans. Amer. Math. Soc. 371 (2019), no. 3, 1735-1770.
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Every conformal minimal surface in $\mathbb{R}^3$ is isotopic to the real part of a holomorphic null curve
Antonio Alarcón and Franc Forstnerič
J. Reine Angew. Math. (Crelle's J.) 740 (2018), 77-109.
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Complete densely embedded complex lines in $\mathbb{C}^2$
Antonio Alarcón and Franc Forstnerič
Proc. Amer. Math. Soc. 146 (2018), no. 3, 1059-1067.
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Complete minimal surfaces densely lying in arbitrary domains of $\mathbb{R}^n$
Antonio Alarcón and Ildefonso Castro-Infantes
Geom. Topol. 22 (2018), no. 1, 571-590.
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Proper holomorphic Legendrian curves in $SL_2(\mathbb{C})$
Antonio Alarcón
J. Geom. Anal. 27 (2017), no. 4, 3013-3029.
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Representing de Rham cohomology classes on an open Riemann surface by holomorphic forms
Antonio Alarcón and Finnur Lárusson
Internat. J. Math. 28 (2017), no. 9, 1740004 (12 pp.).
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Complete embedded complex curves in the ball of $\mathbb{C}^2$ can have any topology
Antonio Alarcón and Josip Globevnik
Anal. PDE 10 (2017), no. 8, 1987-1999.
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Holomorphic Legendrian curves
Antonio Alarcón, Franc Forstnerič, and Francisco J. López
Compos. Math. 153 (2017), no. 9, 1945-1986.
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Embedded minimal surfaces in $\mathbb{R}^n$
Antonio Alarcón, Franc Forstnerič, and Francisco J. López
Math. Z. 283 (2016), no. 1-2, 1-24.
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Complete bounded embedded complex curves in $\mathbb{C}^2$
Antonio Alarcón and Francisco J. López
J. Eur. Math. Soc. (JEMS) 18 (2016), no. 8, 1675-1705.
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The Minkowski problem, new constant curvature surfaces in $\mathbb{R}^3$, and some applications
Antonio Alarcón and Rabah Souam
J. Reine Angew. Math. (Crelle's J.) 710 (2016), 1-19.
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Every bordered Riemann surface is a complete conformal minimal surface bounded by Jordan curves
Antonio Alarcón, Barbara Drinovec Drnovšek, Franc Forstnerič, and Francisco J. López
Proc. Lond. Math. Soc. 111 (2015), no. 4, 851-886.
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Capillary surfaces inside polyhedral regions
Antonio Alarcón and Rabah Souam
Calc. Var. Partial Differential Equations 54 (2015), no. 2, 2149-2166.
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The Calabi-Yau problem, null curves, and Bryant surfaces
Antonio Alarcón and Franc Forstnerič
Math. Ann. 363 (2015), no. 3, 913-951.
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Approximation theory for non-orientable minimal surfaces and applications
Antonio Alarcón and Francisco J. López
Geom. Topol. 19 (2015), no. 2, 1015-1062.
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Null holomorphic curves in $\mathbb{C}^3$ and applications to the conformal Calabi-Yau problem
Antonio Alarcón and Franc Forstnerič
In Complex Geometry and Dynamics: The Abel Symposium 2013, Abel Symposia 10 (2015), 101-121. Springer-Verlag, Berlin-Heidelberg. (Research-expository article.)
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Null curves and directed immersions of open Riemann surfaces
Antonio Alarcón and Franc Forstnerič
Invent. Math. 196 (2014), no. 3, 733–771.
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Complete non-orientable minimal surfaces in $\mathbb{R}^3$ and asymptotic behavior
Antonio Alarcón and Francisco J. López
Anal. Geom. Metr. Spaces 2 (2014), 214-234.
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Properness of associated minimal surfaces
Antonio Alarcón and Francisco J. López
Trans. Amer. Math. Soc. 366 (2014), no. 10, 5139-5154.
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Harmonic diffeomorphisms between domains in the Euclidean 2-sphere
Antonio Alarcón and Rabah Souam
Comment. Math. Helv. 89 (2014), no. 1, 255-271.
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Every bordered Riemann surface is a complete proper curve in a ball
Antonio Alarcón and Franc Forstnerič
Math. Ann. 357 (2013), no. 3, 1049-1070.
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Compact complete null curves in Complex 3-space
Antonio Alarcón and Francisco J. López
Israel J. Math. 195 (2013), no. 1, 97-122.
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Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into $\mathbb{C}^2$
Antonio Alarcón and Francisco J. López
J. Geom. Anal. 23 (2013), no. 4, 1794-1805.
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On harmonic quasiconformal immersions of surfaces in $\mathbb{R}^3$
Antonio Alarcón and Francisco J. López
Trans. Amer. Math. Soc. 365 (2013), no. 4, 1711-1742.
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Harmonic mappings and conformal minimal immersions of Riemann surfaces into $\mathbb{R}^N$
Antonio Alarcón, Isabel Fernández, and Francisco J. López
Calc. Var. Partial Differential Equations 47 (2013), no. 1-2, 227-242.
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Null curves in $\mathbb{C}^3$ and Calabi-Yau conjectures
Antonio Alarcón and Francisco J. López
Math. Ann. 355 (2013), no. 2, 429-455.
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Maximal surfaces and harmonic diffeomorphisms
Antonio Alarcón and Rabah Souam
Pure and Applied Differential Geometry PADGE 2012 - In Memory of Franki Dillen, p. 13-19. (Research-expository article.)
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Complete minimal surfaces and harmonic functions
Antonio Alarcón, Isabel Fernández, and Francisco J. López
Comment. Math. Helv. 87 (2012), no. 4, 891-904.
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Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$
Antonio Alarcón and Francisco J. López
J. Differential Geom. 90 (2012), no. 3, 351-382.
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Inmersiones armónicas de superficies de Riemann en $\mathbb{R}^3$
Antonio Alarcón and Francisco J. López
Florentino García Santos: In memoriam. Universidad de Granada, 2011, p. 1-8. (Research-expository article.)
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Proper harmonic maps from hyperbolic Riemann surfaces into the Euclidean plane
Antonio Alarcón and José A. Gálvez
Results Math. 60 (2011), no. 1-4, 487-505.
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Complete minimal surfaces in $\mathbb{R}^3$ with a prescribed coordinate function
Antonio Alarcón and Isabel Fernández
Differential Geom. Appl. 29 (2011), s. 1, S9-S15.
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Compact complete proper minimal immersions in strictly convex bounded regular domains of $\mathbb{R}^3$
Antonio Alarcón
AIP Conf. Proc. 1260 (2010), 105-111.
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Compact complete minimal immersions in $\mathbb{R}^3$
Antonio Alarcón
Trans. Amer. Math. Soc. 362 (2010), no. 8, 4063-4076.
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On the Calabi-Yau problem for maximal surfaces in $\mathbb{L}^3$
Antonio Alarcón
Differential Geom. Appl. 26 (2008), no. 6, 625-634.
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Limit sets for complete minimal immersions
Antonio Alarcón and Nikolai Nadirashvili
Math. Z. 258 (2008), no. 1, 107-113.
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On the existence of a proper conformal maximal disk in $\mathbb{L}^3$
Antonio Alarcón
Differential Geom. Appl. 26 (2008), no. 2, 151-168.
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Density theorems for complete minimal surfaces in $\mathbb{R}^3$
Antonio Alarcón, Leonor Ferrer, and Francisco Martín
Geom. Funct. Anal. 18 (2008), no. 1, 1-49.
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A uniqueness theorem for the singly periodic genus-one helicoid
Antonio Alarcón, Leonor Ferrer, and Francisco Martín
Trans. Amer. Math. Soc. 359 (2007), no. 6, 2819-2829.
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Recent progresses in the Calabi-Yau problem for minimal surfaces
Antonio Alarcón
Mat. Contemp. 30 (2006), 29-40. (Research-expository article.)