Published papers and books

  1. Joaquín Pérez & Antonio Ros, SOME UNIQUENESS AND NONEXISTENCE THEOREMS FOR EMBEDDED MINIMAL SURFACES, Mathematische Annalen, vol 295 (1993) 513-525 pdf (151 KB).
  2. Joaquín Pérez & Antonio Ros, THE SPACE OF PROPERLY EMBEDDED MINIMAL SURFACES WITH FINITE TOTAL CURVATURE, Indiana University Mathematical Journal, vol. 45 Number 1 (1996) 177-204 pdf (264 KB).
  3. Joaquín Pérez, ON SINGLY PERIODIC MINIMAL SURFACES WITH PLANAR ENDS, Transactions of the AMS, vol. 349 Number 6 (1997) 2371-2389 pdf(259 KB).
  4. Joaquín Pérez, RIEMANN BILINEAR RELATIONS ON MINIMAL SURFACES, Mathematische annalen, vol. 310 (1998) 307-332 pdf (268 KB).
  5. William H. Meeks III, Joaquín Pérez & Antonio Ros, UNIQUENESS OF THE RIEMANN MINIMAL EXAMPLES, Inventiones Mathematicae, vol. 131 (1998) 107-132 pdf (281 KB).
  6. Joaquín Pérez, A RIGIDITY THEOREM FOR PERIODIC MINIMAL SURFACES, Communications in Analysis and Geometry, vol. 7 Number 1 (1999) 95-104 pdf(125 KB).
  7. Joaquín Pérez & Antonio Ros, THE SPACE OF COMPLETE MINIMAL SURFACES WITH FINITE TOTAL CURVATURE AS LAGRANGIAN SUBMANIFOLD, Transactions of the AMS, vol. 351 Number 10 (1999) 3935-3952 pdf (212 KB).
  8. Laurent Hauswirth, Joaquín Pérez & Pascal Romon, EMBEDDED MINIMAL ENDS OF FINITE TYPE, Transactions of the AMS, vol. 353 Number 4 (2001) 1335-1370 pdf (449 KB).
  9. Joaquín Pérez & Antonio Ros, PROPERLY EMBEDDED MINIMAL SURFACES WITH FINITE TOTAL CURVATURE, in THE GLOBAL THEORY OF MINIMAL SURFACES IN FLAT SPACES, Lecture Notes in Mathematics, Springer-Verlag Vol. 1775 (2002) 15-66 pdf (850 KB).
  10. Joaquín Pérez & Antonio Ros, PROPERLY EMBEDDED MINIMAL ANNULI BOUNDED BY A CONVEX CURVE, Journal de l’Institut Mathématique de Jussieu, vol. 1 Number 2 (2002) 293-305 pdf (174 KB).
  11. Francisco J. López & Joaquín Pérez, PARABOLICITY AND GAUSS MAP OF MINIMAL SURFACES, Indiana University Mathematical Journal, vol. 4 Number 52 (2003) 1017-1026 pdf (143 KB).
  12. Francisco Martín & Joaquín Pérez, SUPERFICIES MINIMALES FOLIADAS POR CIRCUNFERENCIAS: LOS EJEMPLOS DE RIEMANN, Gaceta de la R.S.M.E. Vol. 6 Number 3 (2003) 571-596 pdf (4568 KB).
  13. Laurent Hauswirth, Joaquín Pérez, Pascal Romon & Antonio Ros, THE PERIODIC ISOPERIMETRIC PROBLEM, Transactions of the AMS, vol. 356 (2004) 2025-2047 pdf (433 KB).
  14. William H. Meeks III, Joaquín Pérez & Antonio Ros, THE GEOMETRY OF MINIMAL SURFACES OF FINITE GENUS I; CURVATURE ESTIMATES AND QUASIPERIODICITY, Journal of Differential Geometry, vol. 66 (2004) 1-45 pdf (447 KB).
  15. William H. Meeks III, Joaquín Pérez & Antonio Ros, THE GEOMETRY OF MINIMAL SURFACES OF FINITE GENUS II; NONEXISTENCE OF ONE LIMIT END EXAMPLES, Inventiones Mathematicae, vol. 158 (2004) 323-341 pdf (176 KB).
  16. William H. Meeks III & Joaquín Pérez, CONFORMAL PROPERTIES IN CLASSICAL MINIMAL SURFACE THEORY, in Surveys in Differential Geometry, Volume IX (2004): Eigenvalues of Laplacians and other geometric operators. Pages 275-335, DOI: https://dx.doi.org/10.4310/SDG.2004.v9.n1.a8.
    Editors: Alexander Grigor’yan and S. T. Yau, International Press. ISBN: 1-57146-115-9.     pdf (557 KB).
  17. Joaquín Pérez, Magdalena Rodríguez & Martin Traizet, THE CLASSIFICATION OF DOUBLY PERIODIC MINIMAL TORI WITH PARALLEL ENDS, Journal of Differential Geometry, vol. 69 Number 3 (2005) 523-577 pdf (1,29 MB).
  18. William H. Meeks III, Joaquín Pérez & Antonio Ros, LIOUVILLE TYPE PROPERTIES FOR EMBEDDED MINIMAL SURFACES, Communications in Analysis and Geometry, vol 14 Number 4 (2006) 703-723 pdf (164 KB).
  19. Joaquín Pérez & Martin Traizet, THE CLASSIFICATION OF SINGLY PERIODIC MINIMAL SURFACES WITH GENUS ZERO AND SCHERK TYPE ENDS, Transactions of the AMS, vol 359 number 3 (2007) 965-990 pdf (692 KB).
  20. Joaquín Pérez, STABLE EMBEDDED MINIMAL SURFACES BOUNDED BY A STRAIGHT LINE, Calculus of Variations and Partial Differential Equations, vol. 29 Number 2 (2007) 267-279 pdf (418 KB).
  21. William H. Meeks III, Joaquín Pérez & Antonio Ros, STABLE CONSTANT MEAN CURVATURE SURFACES, in Handbook of Geometric Analysis nº 1 (2008). Editors: Lizhen Ji, Peter Li, Richard Schoen, Leon Simon. International Press. ISBN: 978-1-57146-130-8 pdf (1,7 MB).
  22. William H. Meeks III & Joaquín Pérez, PROPERLY EMBEDDED MINIMAL PLANAR DOMAINS WITH INFINITE TOPOLOGY ARE RIEMANN MINIMAL EXAMPLES, Current Developments in Mathematics 2008, Editors: David Jenson, Barry Mazur, Tornasz Mrowka, Wilfried Schmid, Richard P. Stanley, Shing-Tung Yau. International Press. ISBN -13: 978-1-57146-139-1 arxiv pdf (695 KB).
  23. William H. Meeks III, Joaquín Pérez & Antonio Ros, LIMIT LEAVES OF AN H-LAMINATION ARE STABLE, Journal of Differential Geometry, vol. 84 (2010) 179-189  Arxiv link (310 KB).
  24. J. Miguel Manzano, Joaquín Pérez & M. Magdalena Rodríguez, PARABOLIC STABLE SURFACES WITH CONSTANT MEAN CURVATURE, Calculus of Variations and Partial Differential Equations, vol. 42 (2011) 137-152 Arxiv link (465 KB).
  25. William H. Meeks III & Joaquín Pérez, THE CLASSICAL THEORY OF MINIMAL SURFACES, Bulletin of the AMS, vol. 48 (2011) 325-407 pdf(3 MB).
  26. Joaquín Pérez, SINH-GORDON TYPE EQUATIONS FOR CMC SURFACES, Florentino García Santos: In memoriam, Universidad de Granada (2011) pdf(330 KB).
  27. William H. Meeks III, Joaquín Pérez, A SURVEY ON CLASSICAL MINIMAL SURFACE THEORY, University Lecture Series (AMS) vol. 60 (2012) 182 pages. ISBN: 978-0-82 pdf (3,5 MB).
  28. William H. Meeks III & Joaquín Pérez, CONSTANT MEAN CURVATURE SURFACES IN METRIC LIE GROUPS, in »Geometric Analysis: Partial Differential Equations and Surfaces», Contemporary Mathematics (AMS) vol. 570 (2012) 25-110 pdf (2.142 KB).
  29. William H. Meeks III, Pablo Mira, Joaquín Pérez & Antonio Ros, ISOPERIMETRIC DOMAINS OF LARGE VOLUME IN HOMOGENEOUS THREE-MANIFOLDS, Advances in Mathematics, vol 264 (2014) 546–592, Arxiv link (702 KB).
  30. William H. Meeks III, Joaquín Pérez & Antonio Ros, PROPERLY EMBEDDED MINIMAL PLANAR DOMAINS, Annals of Mathematics,  vol. 181 no. 2 (2015) 473-546, Arxiv link (1,1 MB).
  31. William H. Meeks III & Joaquín Pérez, CMC FOLIATIONS OF CLOSED MANIFOLDS, The Journal of Geometric Analysis, vol. 26 no. 3 (July 2016) 1647-1677, Arxiv link, https://rdcu.be/6yOH
  32. William H. Meeks III, Joaquín Pérez & Antonio Ros, LOCAL REMOVABLE SINGULARITY THEOREMS FOR MINIMAL LAMINATIONS, Journal of Differential Geometry, vol. 103 (2016) 319-362, Arxiv link (536 KB).
  33. William H. Meeks III, Joaquín Pérez & Antonio Ros, THE DYNAMICS THEOREM FOR PROPERLY EMBEDDED MINIMAL SURFACES, Matematische Annalen, vol. 365, no. 3 (August 2016) 1069-1089Arxiv link (549 KB), https://rdcu.be/56NO
  34. William H. Meeks III & Joaquín Pérez, THE RIEMANN MINIMAL EXAMPLES. Chapter in the book ‘The Legacy of Bernhard Riemann After One Hundred and Fifty Years’, Advanced Lectures in Mathematics nº 35 (2016) 417-457, Higher Education Press (Beijing) and International Press (Boston).  ISBN: 978-704-031875-3. Edited by Lizhen Ji, Frans Oort and Shing-Tung Yau. pdf (533 KB).
  35. William H. Meeks III, Joaquín Pérez & Antonio Ros, THE CLASSIFICATION OF CMC FOLIATIONS OF \(\mathbb{R}^3\) AND \(\mathbb{S}^3\) WITH COUNTABLY MANY SINGULARITIES, American Journal of Mathematics, vol. 138, no. 5 (2016) 1347-1382, Arxiv link 
  36. William H. Meeks III, Joaquín Pérez & Giuseppe Tinaglia, CONSTANT MEAN CURVATURE SURFACES, Surveys in Differential Geometry, vol 21 (2016) 179-287, International Press, pdf (2,9 MB).
  37. Joaquín Pérez, UNA NUEVA EDAD DE ORO DE LAS SUPERFICIES MINIMAS, Gaceta de la RSME, vol. 20, no. 5 (2017) 193-211, pdf (151 KB).
  38. Joaquín Pérez, A NEW GOLDEN AGE OF MINIMAL SURFACES, Notices of the AMS, vol. 64, no. 4 (2017) 347-358, pdf (1,9 MB).
  39. William H. Meeks III & Joaquín Pérez, FINITE TYPE ANNULAR ENDS FOR HARMONIC FUNCTIONS, Mathematische Annalen, vol. 367, no. 3 (2017) 1047-1056. DOI:10.1007/s00208-016-1407-0. Arxiv link (447 KB), https://rdcu.be/56PT
  40. William H. Meeks III, Pablo Mira & Joaquín Pérez, EMBEDDEDNESS OF SPHERES IN HOMOGENEOUS THREE-MANIFOLDS, International Mathematics Research Notices, vol. 2017, no. 15 (2017) 4796–4813. Advance Access Publication July 20, 2016 DOI: 10.1093/imrn/rnw159, online version, Arxiv link 
  41. William H. Meeks III & Joaquín Pérez, FINITE TOPOLOGY MINIMAL SURFACES IN HOMOGENEOUS THREE-MANIFOLDS, Advances in Mathematics, vol. 312 (2017) 185-197 (https://doi.org/10.1016/j.aim.2017.03.015), Arxiv link
  42. William H. Meeks III, Joaquín Pérez & Antonio Ros, THE LOCAL PICTURE THEOREM ON THE SCALE OF TOPOLOGY, Journal of Differential Geometry, vol. 109, no. 3 (2018) 509-565, Arxiv link (937 KB).
  43. William H. Meeks III & Joaquín Pérez, EMBEDDED MINIMAL SURFACES OF FINITE TOPOLOGY, Journal für Reine und Angewandte Mathematik, vol. 753 (2019) 159-191 (DOI: 10.1515/crelle-2017-0008), Arxiv link
  44. William H. Meeks III, Pablo Mira & Joaquín Pérez, THE GEOMETRY OF STABLE MINIMAL SURFACES IN METRIC LIE GROUPS, Transactions of the AMS, vol. 372, no. 2 (2019) 1023-1056. DOI: https://doi.org/10.1090/tran/7634, Arxiv link
  45. William H. Meeks III, Joaquín Pérez & Antonio Ros, STRUCTURE THEOREMS FOR SINGULAR MINIMAL LAMINATIONS, Journal für die Reine und Angewandte Mathematik (Crelles Journal), vol. 2020, no. 763, 2020, pp. 271-312, DOI: 10.1515/crelle-2018-0036, Arxiv link 
  46. William H. Meeks III, Joaquín Pérez & Antonio Ros, BOUNDS ON THE TOPOLOGY AND INDEX OF MINIMAL SURFACES, Acta Mathematica, vol. 223 (2019) 113–149. DOI: 10.4310/ACTA.2019.v223.n1.a2 Arxiv link
  47. William H. Meeks III, Pablo Mira, Joaquín Pérez & Antonio Ros, CONSTANT MEAN CURVATURE SPHERES IN HOMOGENEOUS THREE-SPHERES, Journal of Differential Geometry, vol. 120, No. 2 (2022) 307-343. DOI 10.4310/jdg/1645207520 Arxiv link 
  48. William H. Meeks III, Pablo Mira, Joaquín Pérez & Antonio Ros, CONSTANT MEAN CURVATURE SPHERES IN HOMOGENEOUS THREE-MANIFOLDS, Inventiones Mathematicae, vol. 224 (2021) 147–244. DOI https://doi.org/10.1007/s00222-020-01008-y Full-text (open access) version, HTML version
  49. William H. Meeks III, Joaquín Pérez & Antonio Ros, THE EMBEDDED CALABI-YAU CONJECTURE FOR FINITE GENUS, Duke Math. J. 170(13) (2021) 2891-2956. DOI: 10.1215/00127094-2020-0087. Arxiv link
  50. David Moya & Joaquín Pérez, GENERALIZED HENNEBERG STABLE MINIMAL SURFACES, Results in Mathematics, https://doi.org/10.1007/s00025-022-01831-0. ArXiv link
  51. William H. Meeks III & Joaquín Pérez, HIERARCHY STRUCTURES IN FINITE INDEX CMC SURFACES, Advances in Calculus of Variations, 2023. https://doi.org/10.1515/acv-2022-0113. Arxiv link
  52. William H. Meeks III & Joaquín Pérez, GEOMETRY OF CMC SURFACES OF FINITE INDEX, Advanced Nonlinear Studies, vol. 23, no. 1, 2023, pp. 20220063. https://doi.org/10.1515/ans-2022-0063 Golden open access link
  53. Pablo Mira & Joaquín Pérez, UNIQUENESS OF CONSTANT MEAN CURVATURE SPHERES, in NEW TRENDS IN GEOMETRIC ANALYSIS, Spanish Network of Geometric Analysis 2007-2021, RSME-Springer Nature series, vol. 10. (2023) 365-393. https://doi.org/10.1007/978-3-031-39916-9
  54. William H. Meeks III & Joaquín Pérez, GEOMETRY OF BRANCHED MINIMAL SURFACES OF FINITE INDEX, Advanced Nonlinear Studies, special issue in honor of Joel Spruck, 2024. https://doi.org/10.1515/ans-2023-0118. Arxiv link

Preprints, work in progress

  1. José M. Espinar, José A. Gálvez & Joaquín Pérez, FREE BOUNDARY MINIMAL SURFACES WITH ANTIPRISMATIC SYMMETRY AND ONE BOUNDARY COMPONENT (work in progress)
  2. William H. Meeks III & Joaquín Pérez, CMC FOLIATIONS OF COMPACT THREE-MANIFOLDS (work in progress)
  3. William H. Meeks III & Joaquín Pérez, CLASSICAL MINIMAL SURFACES IN HOMOGENEOUS THREE-MANIFOLDS (work in progress)
  4. William H. Meeks III, Joaquín Pérez & Antonio Ros, MINIMAL SURFACES WHOSE GAUSS MAP MISSES FOUR POINTS (work in progress)

Proceedings in Conferences

  1. Joaquín Pérez & Antonio Ros, PROPERLY EMBEDDED MINIMAL SURFACES WITH FINITE TOTAL CURVATURE, Proceedings of the 1995 Conference «Geometry and topology of submanifolds VIII» World Scientific (1996) 280-281.
  2. Joaquín Pérez, STRONG RIGIDITY AND PERIODIC MINIMAL SURFACES, Proceedings of the 1997 Conference «1st International Meeting on Geometry and Topology» A. Pereira do Vale & M. R Pinto (Ed.) (1998) 169-173.
  3. Joaquín Pérez, PARABOLICITY AND MINIMAL SURFACES, Proceedings of The Clay Mathematics Institute 2001 Summer School «The global theory of minimal surfaces», Mathematical Sciences Research Institute, Berkeley (California) Editor: David Hoffman ISBN: 9780821835876 pags. 163-174. pdf (214 KB).
  4. Joaquín Pérez, UNIQUENESS OF THE RIEMANN MINIMAL SURFACES, Proceedings of The Clay Mathematics Institute 2001 Summer School «The global theory of minimal surfaces», Mathematical Sciences Research Institute, Berkeley (California) Editor: David Hoffman ISBN: 9780821835876 pags 697-610. pdf (276 KB).
  5. Joaquín Pérez, LIMITS BY RESCALING OF MINIMAL SURFACES: MINIMAL LAMINATIONS, CURVATURE DECAY AND LOCAL PICTURES, notes for the workshop «Moduli Spaces of Properly Embedded Minimal Surfaces», American Institute of Mathematics, Palo Alto, California (2005)pdf (726 KB).
  6. Joaquín Pérez, EXTINCION EN TIEMPO FINITO DEL FLUJO DE RICCI, notas para la Escuela avanzada sobre la Conjetura de Poincaré, Granada (2007) pdf (473 KB).

Slides of talks

  1. Joaquín Pérez, INTRODUCTION TO SURFACE THEORY IN METRIC LIE GROUPS, doc-Course in the Advanced School «Submanifold Theory and Applications», IMUS 2011 pdf (2,67 MB).

Others

  1. Joaquín Pérez, SUPERFICIES MINIMALES EN R^3, Tesis Doctoral – Universidad de Granada (1996).
  2. Joaquín Pérez, NOTAS SOBRE GEOMETRIA RIEMANNIANA GLOBAL (2000).
  3. Joaquín Pérez, APUNTES DE GEOMETRIA RIEMANNIANA (2004). Correspondientes a la asignatura optativa de 2º ciclo «Geometría Riemanniana» (4º curso de la Licenciatura de Matemáticas de la UGR, 1er cuatrimestre), impartida durante el período 2004-2007. pdf (850 KB).Nota: El formato actual de la asignatura podría no coincidir con estos apuntes.
  4. Joaquín Pérez, APUNTES DE GEOMETRIA y TOPOLOGIA (2007). Correspondientes a la asignatura obligatoria de 2º ciclo «Geometría y Topología» (4º curso de la Licenciatura de Matemáticas de la UGR), impartida durante el período 2008-2010. pdf (1,1 MB). Nota: El formato actual de la asignatura podría no coincidir con estos apuntes.
  5. Joaquín Pérez, APUNTES DE GEOMETRIA DE CONVEXOS (2013). Correspondientes a la asignatura optativa de 2º ciclo «Geometría de Convexos» (5º curso de la Licenciatura de Matemáticas de la UGR, 1er cuatrimestre), impartida durante el período 2012-2014. pdf (1,1 MB).
  6. Joaquín Pérez, APUNTES DE CURVAS Y SUPERFICIES (2017). Correspondientes a la asignatura obligatoria de 2º curso «Curvas y Superficies» del Grado en Matemáticas de la UGR, 2º cuatrimestre), impartida durante el período 2014-2017. pdf (1,7 MB). Nota: El formato actual de la asignatura podría no coincidir con estos apuntes.
  7. Joaquín Pérez, SUPERFICIES MINIMAS Y DE CURVATURA MEDIA CONSTANTE (Curso basado en el principio del máximo, 2014). pdf (2,4 MB).
  8. Joaquín Pérez, MINIMAL AND CONSTANT MEAN CURVATURE SURFACES (2019, versión traducida al inglés y actualizada de las notas de 2017). pdf (4,7 MB).
  9. Joaquín Pérez, APUNTES DE GEOMETRIA II (2018). pdf (472 KB).