Publications

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Updated at November 2025

Profiles

                                   

Books

• New Trends in Geometric Analysis. Spanish Network of Geometric Analysis 2007-2021
  Antonio Alarcón, Vicente Palmer, and César Rosales (editors)
  RSME Springer Series 10
  Springer, Cham, 2023, viii+393 pp.
  ISBN: 978-3-031-39915-2 (print); 978-3-031-39916-9 (online).
• Minimal Surfaces from a Complex Analytic Viewpoint
  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

• Removing singularities of minimal surfaces by isotopies
  Antonio Alarcón and Franc Forstnerič
  Preprint, 2025.
• Holomorphic null curves in the special linear group
  Antonio Alarcón and Jorge Hidalgo
  Trans. Amer. Math. Soc., in press. Arxiv.
• On the Gauss map assignment for minimal surfaces and the Osserman curvature estimate
  Antonio Alarcón and Francisco J. López
  Ann. Mat. Pura Appl., in press. Full text view only (First View). Arxiv.
• Generic properties of minimal surfaces
  Antonio Alarcón and Francisco J. López
  Proc. Roy. Soc. Edinburgh Sect. A, in press. Open access link (First View). Arxiv. Digibug.
• 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. Arxiv.
• Complete minimal surfaces with Cantor ends in minimally convex domains
  Antonio Alarcón
  Pure Appl. Funct. Anal., in press. (Issue dedicated to Nikolai Nadirashvili.) Arxiv.
• Isotopies of complete minimal surfaces of finite total curvature
  Antonio Alarcón, Franc Forstnerič, and Finnur Lárusson
  Preprint, 2024.
• Proper harmonic embeddings of open Riemann surfaces into R⁴
  Antonio Alarcón and Francisco J. López
  Preprint, 2022.

Papers 2019-Today

• Oka-1 manifolds
  Antonio Alarcón and Franc Forstnerič
  Math. Z. 311 (2025), no. 2, Paper No. 33. Open access link. Arxiv. Digibug.
• Regular immersions directed by algebraically elliptic cones
  Antonio Alarcón and Finnur Lárusson
  J. Reine Angew. Math. (Crelle's J.) 823 (2025), 113-135. Arxiv.
• A strong parametric h-principle for complete minimal surfaces
  Antonio Alarcón and Finnur Lárusson
  J. Geom. Anal. 35 (2025), no. 2, Paper No. 42. Full text view only. Arxiv.
• 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. Arxiv.
• Hipersuperficies complejas completas en la bola de Cⁿ
  Antonio Alarcón
  Gac. R. Soc. Mat. Esp. 27 (2024), no. 3, 477-496. (Research-expository article, in Spanish.) Open access link. Digibug.
• Embedded complex curves in the affine plane
  Antonio Alarcón and Franc Forstnerič
  Ann. Mat. Pura Appl. 203 (2024), no. 4, 1673-1701. Open access link. Arxiv. Digibug.
• 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. Arxiv.
• Complete nonsingular holomorphic foliations on Stein manifolds
  Antonio Alarcón and Franc Forstnerič
  Mediterr. J. Math. 21 (2024), no. 1, 25. Open access link. Arxiv. Digibug.
• 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.) Full text view only. Arxiv.
• Wild holomorphic foliations of the ball
  Antonio Alarcón
  Indiana Univ. Math. J. 71 (2022), no. 2, 561-578. ArXiv.
• Algebraic approximation and the Mittag-Leffler theorem for minimal surfaces
  Antonio Alarcón and Francisco J. López
  Anal. PDE 15 (2022), no. 3, 859-890. ArXiv.
• Complete complex hypersurfaces in the ball come in foliations
  Antonio Alarcón
  J. Differential Geom. 121 (2022), no. 1, 1-29. ArXiv.
• Holomorphic Legendrian curves in CP³ and superminimal surfaces in S⁴
  Antonio Alarcón, Franc Forstnerič, and Finnur Lárusson
  Geom. Topol. 25 (2021), no. 7, 3507-3553. ArXiv.
• 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. ArXiv.
• A foliation of the ball by complete holomorphic discs
  Antonio Alarcón and Franc Forstnerič
  Math. Z. 296 (2020), no. 1-2, 169-174. Full text view only. ArXiv.
• Complex curves in pseudoconvex Runge domains containing discrete subsets
  Antonio Alarcón
  J. Anal. Math. 140 (2020), no. 1, 207-226. Full text view only. ArXiv.
• New complex analytic methods in the study of non-orientable minimal surfaces in Rⁿ
  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). ArXiv.
• 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. Full text view only. ArXiv.
• 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. ArXiv.
• 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.) Full text view only. ArXiv.
• Darboux charts around holomorphic Legendrian curves and applications
  Antonio Alarcón and Franc Forstnerič
  Int. Math. Res. Not. IMRN 2019 (2019), no. 3, 893-922. Free-access link. ArXiv.
• 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. Full text view only. ArXiv.
  Correction, Calc. Var. Partial Differential Equations 59 (2020), no. 5, 59:178. Free-access link. ArXiv.
• Interpolation by conformal minimal surfaces and directed holomorphic curves
  Antonio Alarcón and Ildefonso Castro-Infantes
  Anal. PDE 12 (2019), no. 2, 561-604. ArXiv.
• 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. ArXiv.

Papers 2006-2018

• Every conformal minimal surface in R³ 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. ArXiv.
• Complete densely embedded complex lines in C²
  Antonio Alarcón and Franc Forstnerič
  Proc. Amer. Math. Soc. 146 (2018), no. 3, 1059-1067. ArXiv.
• Complete minimal surfaces densely lying in arbitrary domains of Rⁿ
  Antonio Alarcón and Ildefonso Castro-Infantes
  Geom. Topol. 22 (2018), no. 1, 571-590. ArXiv.
• Proper holomorphic Legendrian curves in SL₂(C)
  Antonio Alarcón
  J. Geom. Anal. 27 (2017), no. 4, 3013-3029. Full text view only. ArXiv.
• 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.). ArXiv.
• Complete embedded complex curves in the ball of C² can have any topology
  Antonio Alarcón and Josip Globevnik
  Anal. PDE 10 (2017), no. 8, 1987-1999. ArXiv.
• Holomorphic Legendrian curves
  Antonio Alarcón, Franc Forstnerič, and Francisco J. López
  Compos. Math. 153 (2017), no. 9, 1945-1986. ArXiv.
• Embedded minimal surfaces in Rⁿ
  Antonio Alarcón, Franc Forstnerič, and Francisco J. López
  Math. Z. 283 (2016), no. 1-2, 1-24. Full text view only. ArXiv.
• Complete bounded embedded complex curves in C²
  Antonio Alarcón and Francisco J. López
  J. Eur. Math. Soc. (JEMS) 18 (2016), no. 8, 1675-1705. ArXiv.
• The Minkowski problem, new constant curvature surfaces in R³, and some applications
  Antonio Alarcón and Rabah Souam
  J. Reine Angew. Math. (Crelle's J.) 710 (2016), 1-19. ArXiv.
• 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. London Math. Soc. 111 (2015), no. 4, 851-886. ArXiv.
• Capillary surfaces inside polyhedral regions
  Antonio Alarcón and Rabah Souam
  Calc. Var. Partial Differential Equations 54 (2015), no. 2, 2149-2166. Full text view only. ArXiv.
• The Calabi-Yau problem, null curves, and Bryant surfaces
  Antonio Alarcón and Franc Forstnerič
  Math. Ann. 363 (2015), no. 3, 913-951. Full text view only. ArXiv.
• Approximation theory for non-orientable minimal surfaces and applications
  Antonio Alarcón and Francisco J. López
  Geom. Topol. 19 (2015), no. 2, 1015-1062. ArXiv.
• Null holomorphic curves in C³ 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.) Full text view only. ArXiv.
• Null curves and directed immersions of open Riemann surfaces
  Antonio Alarcón and Franc Forstnerič
  Invent. Math. 196 (2014), no. 3, 733–771. Full text view only. ArXiv.
• Complete non-orientable minimal surfaces in R³ and asymptotic behavior
  Antonio Alarcón and Francisco J. López
  Anal. Geom. Metr. Spaces 2 (2014), 214-234. ArXiv.
• Properness of associated minimal surfaces
  Antonio Alarcón and Francisco J. López
  Trans. Amer. Math. Soc. 366 (2014), no. 10, 5139-5154. ArXiv.
• Harmonic diffeomorphisms between domains in the Euclidean 2-sphere
  Antonio Alarcón and Rabah Souam
  Comment. Math. Helv. 89 (2014), no. 1, 255-271. ArXiv.
• 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. Full text view only. ArXiv.
• Compact complete null curves in Complex 3-space
  Antonio Alarcón and Francisco J. López
  Israel J. Math. 195 (2013), no. 1, 97-122. Full text view only. ArXiv.
• Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into C²
  Antonio Alarcón and Francisco J. López
  J. Geom. Anal. 23 (2013), no. 4, 1794-1805. Full text view only. ArXiv.
• On harmonic quasiconformal immersions of surfaces in R³
  Antonio Alarcón and Francisco J. López
  Trans. Amer. Math. Soc. 365 (2013), no. 4, 1711-1742. ArXiv.
• Harmonic mappings and conformal minimal immersions of Riemann surfaces into R^N
  Antonio Alarcón, Isabel Fernández, and Francisco J. López
  Calc. Var. Partial Differential Equations 47 (2013), no. 1-2, 227-242. Full text view only. ArXiv.
• Null curves in C³ and Calabi-Yau conjectures
  Antonio Alarcón and Francisco J. López
  Math. Ann. 355 (2013), no. 2, 429-455. Full text view only. ArXiv.
• 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.) pdf.
• Complete minimal surfaces and harmonic functions
  Antonio Alarcón, Isabel Fernández, and Francisco J. López
  Comment. Math. Helv. 87 (2012), no. 4, 891-904. ArXiv.
• Minimal surfaces in R³ properly projecting into R²
  Antonio Alarcón and Francisco J. López
  J. Differential Geom. 90 (2012), no. 3, 351-382. ArXiv.
• Inmersiones armónicas de superficies de Riemann en R³
  Antonio Alarcón and Francisco J. López.
  Florentino García Santos: In memoriam. Universidad de Granada, 2011, p. 1-8. (Research-expository article.)
• 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. Full text view only. ArXiv.
• Complete minimal surfaces in R³ with a prescribed coordinate function
  Antonio Alarcón and Isabel Fernández
  Differential Geom. Appl. 29 (2011), s. 1, S9-S15. ArXiv.
• Compact complete proper minimal immersions in strictly convex bounded regular domains of R³
  Antonio Alarcón
  AIP Conf. Proc. 1260 (2010), 105-111. pdf.
• Compact complete minimal immersions in R³
  Antonio Alarcón
  Trans. Amer. Math. Soc. 362 (2010), no. 8, 4063-4076. ArXiv.
• On the Calabi-Yau problem for maximal surfaces in L³
  Antonio Alarcón
  Differential Geom. Appl. 26 (2008), no. 6, 625-634. ArXiv.
• Limit sets for complete minimal immersions
  Antonio Alarcón and Nikolai Nadirashvili
  Math. Z. 258 (2008), no. 1, 107-113. Full text view only. ArXiv.
• On the existence of a proper conformal maximal disk in L³
  Antonio Alarcón
  Differential Geom. Appl. 26 (2008), no. 2, 151-168. ArXiv.
• Density theorems for complete minimal surfaces in R³
  Antonio Alarcón, Leonor Ferrer, and Francisco Martín
  Geom. Funct. Anal. 18 (2008), no. 1, 1-49. ArXiv.
• 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. ArXiv.
• Recent progresses in the Calabi-Yau problem for minimal surfaces
  Antonio Alarcón
  Mat. Contemp. 30 (2006), 29-40. (Research-expository article.) pdf.
• On the singly periodic genus one helicoid
  Antonio Alarcón, Leonor Ferrer, and Francisco Martín
  Differ. Geom. Dyn. Syst. 8 (2006), 1-7. pdf.

Ph.D. Thesis

• Superficies Minimales Completas en el Espacio Euclídeo
  Antonio Alarcón
  Universidad de Granada (2008) (Spanish).