Publications

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Updated at March 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

• Holomorphic null curves in the special linear group
  Antonio Alarcón and Jorge Hidalgo
  Preprint, 2025.
• On the Gauss map assignment for minimal surfaces and the Osserman curvature estimate
  Antonio Alarcón and Francisco J. López
  Preprint, 2024.
• Generic properties of minimal surfaces
  Antonio Alarcón and Francisco J. López
  Preprint, 2024.
• The Mittag-Leffler theorem for proper minimal surfaces and directed meromorphic curves
  Antonio Alarcón and Tjaša Vrhovnik
  Preprint, 2024.
• 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.
• Regular immersions directed by algebraically elliptic cones
  Antonio Alarcón and Finnur Lárusson
  J. Reine Angew. Math. (Crelle's J.), in press. Arxiv.
• Oka-1 manifolds
  Antonio Alarcón and Franc Forstnerič
  Preprint, 2023.
• Proper harmonic embeddings of open Riemann surfaces into R⁴
  Antonio Alarcón and Francisco J. López
  Preprint, 2022.

Papers 2019-Today

• 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).