Department of Mathematics

Breadcrumb

Nicolaos Kapouleas

Professor
nicolaos_kapouleas@brown.edu
(401) 863-7964
Room 316
Research Interests Differential Geometry, Partial Differential Equations

Biography

Mailing Address

Mathematics Department
Box 1917
Brown University
Providence, RI 02912

Workshops & Seminars

Topics in Differential Geometry Workshop
Brown, University, Providence, RI
March 27-29, 2023

Geometric Analysis Seminar
Thursdays in Kassar 105

Publications

  1. Nikolaos Kapouleas and Jiahua Zou, Index and nullity of minimal surface doublings, I, arXiv:2512.07734 (2025).
  2. Nikolaos Kapouleas and Peter McGrath, New minimal surface doublings of the Clifford torus and contributions to questions of Yau, arXiv:2411.00613v1 (2024).
  3. Nikolaos Kapouleas and Jiahua Zou, Minimal hypersurfaces in S4(1) by doubling the equatorial S3, arXiv:2405.18283v2 (2024).
  4. Nikolaos Kapouleas and David Wiygul, New low-genus desingularizations of three Clif- ford tori and related characterizations, arXiv:2306.09159v2 (2024).
  5. Nikolaos Kapouleas and Peter McGrath, Free boundary minimal annuli immersed in the unit 3-ball, arXiv:2212.09680 (2022).
  6. Nikolaos Kapouleas and Jiahua Zou, Free boundary minimal surfaces in the Euclidean three-ball close to the boundary, Amer. J. Math. (to appear); arXiv:2111.11308 (2021).
  7. Nikolaos Kapouleas and Peter McGrath, Generalizing the Linearized Doubling approach, I: General theory and new minimal surfaces and self-shrinkers, Camb. J. Math. 11 (2023), no. 2, 299–439.
  8. Nikolaos Kapouleas and David Wiygul, Free boundary minimal surfaces with connected boundary in the 3-ball by tripling the equatorial disc, J. Differential Geom. 123 (2023), no. 2, 311–362.
  9. Christine Breiner, Nikolaos Kapouleas, and Stephen Kleene, Conservation laws and gluing constructions for constant mean curvature (hyper)surfaces, Notices Amer. Math. Soc. 69 (2022), no. 5, 762–773. MR4415896
  10. Nikolaos Kapouleas and David Wiygul, The Lawson surfaces are determined by their symmetries and topology, J. Reine Angew. Math. 786 (2022), 155–173. MR4434746
  11. Minimal surfaces in the three-sphere by desingularizing intersecting Clifford tori, Math. Ann. 383 (2022), no. 1-2, 119–170. MR4444117
  12. Christine Breiner and Nikolaos Kapouleas, Complete constant mean curvature hypersur- faces in Euclidean space of dimension four or higher, Amer. J. Math. 143 (2021), no. 4, 1161–1259. MR4291252
  13. Nikolaos Kapouleas and Martin Man-chun Li, Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc, J. Reine Angew. Math. 776 (2021), 201–254. MR4279102
  14. Nikolaos Kapouleas and David Wiygul, The index and nullity of the Lawson surfaces ξg,1, Camb. J. Math. 8 (2020), no. 2, 363–405. MR4091028
  15. Nikolaos Kapouleas and Peter McGrath, Minimal surfaces in the round three-sphere by doubling the equatorial two-sphere, II, Comm. Pure Appl. Math. 72 (2019), no. 10, 2121–2195. MR3998638
  16. Nikolaos Kapouleas, Stephen James Kleene, and Niels Martin Mø ller, Mean curvature self-shrinkers of high genus: non-compact examples, J. Reine Angew. Math. 739 (2018), 1–39. MR3808256
  17. Nikolaos Kapouleas, Minimal surfaces in the round three-sphere by doubling the equatorial two-sphere, I, J. Differential Geom. 106 (2017), no. 3, 393–449. MR3680553
  18. Simon Brendle and Nikolaos Kapouleas, Gluing Eguchi-Hanson metrics and a question of Page, Comm. Pure Appl. Math. 70 (2017), no. 7, 1366–1401. MR3666569
  19. Christine Breiner and Nikolaos Kapouleas, Embedded constant mean curvature surfaces in Euclidean three-space, Math. Ann. 360 (2014), no. 3-4, 1041–1108. MR3273652
  20. Mark Haskins and Nikolaos Kapouleas, The geometry of SO(p)×SO(q)-invariant special Lagrangian cones, Comm. Anal. Geom. 21 (2013), no. 1, 171–250. MR3046941
  21. Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones, Comm. Anal. Geom. 20 (2012), no. 1, 95–162. MR2903102
  22. Nikolaos Kapouleas, Doubling and desingularization constructions for minimal surfaces, Surveys in geometric analysis and relativity, 2011, pp. 281–325. MR2906930
  23. Nikolaos Kapouleas and Seong-Deog Yang, Minimal surfaces in the three-sphere by doubling the Clifford torus, Amer. J. Math. 132 (2010), no. 2, 257–295. MR2654775
  24. Mark Haskins and Nikolaos Kapouleas, Gluing constructions of special Lagrangian cones, Handbook of geometric analysis. No. 1, 2008, pp. 77–145. MR2483363
  25. Special Lagrangian cones with higher genus links, Invent. Math. 167 (2007), no. 2, 223–294. MR2270454
  26. Nikolaos Kapouleas, Constructions of minimal surfaces by gluing minimal immersions, Global theory of minimal surfaces, 2005, pp. 489–524. MR2167274
  27. Complete embedded minimal surfaces of finite total curvature, J. Differential Geom. 47 (1997), no. 1, 95–169. MR1601434
  28. On desingularizing the intersections of minimal surfaces, Proceedings of the 4th International Congress of Geometry (Thessaloniki, 1996), 1997, pp. 34–41. MR1470959
  29. Constant mean curvature surfaces in Euclidean spaces, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Z¨urich, 1994), 1995, pp. 481–490. MR1403948
  30. Constant mean curvature surfaces constructed by fusing Wente tori, Invent. Math. 119 (1995), no. 3, 443–518. MR1317648
  31. Nicolaos Kapouleas, Constant mean curvature surfaces constructed by fusing Wente tori, Proc. Nat. Acad. Sci. U.S.A. 89 (1992), no. 12, 5695–5698. MR1165926
  32. Compact constant mean curvature surfaces in Euclidean three-space, J. Differential Geom. 33 (1991), no. 3, 683–715. MR1100207
  33. Slowly rotating drops, Comm. Math. Phys. 129 (1990), no. 1, 139–159. MR1046281
  34. Complete constant mean curvature surfaces in Euclidean three-space, Ann. of Math. (2) 131 (1990), no. 2, 239–330. MR1043269
  35. Constant mean curvature surfaces in E(3), ProQuest LLC, Ann Arbor, MI, 1988. Thesis (Ph.D.)–University of California, Berkeley. MR2636895
  36. Constant mean curvature surfaces in Euclidean three-space, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 2, 318–320. MR903742

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