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Tytuł artykułu

Complete Non-Orientable Minimal Surfaces in ℝ3and Asymptotic Behavior

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2013-12-02
zaakceptowano
2014-06-17
online
2014-07-26
Twórcy
  • Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain, alarcon@ugr.es
  • Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain, fjlopez@ugr.es
Bibliografia
  • [1] A. Alarcón, Compact complete minimal immersions in R3, Trans. Amer. Math. Soc., 362 (2010), pp. 4063-4076.
  • [2] A. Alarcón, Compact complete proper minimal immersions in strictly convex bounded regular domains of R3, AIP Conference Proceedings, 1260 (2010), pp. 105-111.
  • [3] A. Alarcón and F. J. López, Approximation theory for non-orientable minimal surfaces and applications. Preprint 2013, arXiv:1307.2399 (to appear in Geom. Topol.).
  • [4] A. Alarcón and F. J. López, Properness of associated minimal surfaces. Trans. Amer. Math. Soc., in press.
  • [5] A. Alarcón and F. J. López, Minimal surfaces in R3 properly projecting into R2, J. Di_erential Geom., 90 (2012), pp. 351-381.
  • [6] A. Alarcón and F. J. López, Compact complete null curves in Complex 3-space, Israel J. Math., 195 (2013), pp. 97-122.
  • [7] A. Alarcón and F. J. López, Null curves in C3 and Calabi-Yau conjectures, Math. Ann., 355 (2013), pp. 429-455.[WoS]
  • [8] A. Alarcón and N. Nadirashvili, Limit sets for complete minimal immersions, Math. Z., 258 (2008), pp. 107-113.[WoS]
  • [9] L. Ferrer, F. Martín, and W. H. Meeks, III, Existence of proper minimal surfaces of arbitrary topological type, Adv. Math., 231 (2012), pp. 378-413.[WoS]
  • [10] F. Martín and N. Nadirashvili, A Jordan curve spanned by a complete minimal surface, Arch. Ration. Mech. Anal., 184 (2007), pp. 285-301.[WoS]
  • [11] W. H. Meeks, III, The classi_cation of complete minimal surfaces in R3 with total curvature greater than −8_, Duke Math. J., 48 (1981), pp. 523-535.
  • [12] W. H. Meeks, III and S. T. Yau, The classical Plateau problemand the topology of three-dimensionalmanifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn’s lemma, Topology, 21 (1982), pp. 409-442.
  • [13] H. Minkowski, Volumen und Oberfläche, Math. Ann., 57 (1903), pp. 447-495.
  • [14] N. Nadirashvili, Hadamard’s and Calabi-Yau’s conjectures on negatively curved and minimal surfaces, Invent. Math., 126 (1996), pp. 457-465.
  • [15] R. Schoen and S. T. Yau, Lectures on harmonic maps, Conference Proceedings and Lecture Notes in Geometry and Topology, II, International Press, Cambridge, MA, 1997.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_agms-2014-0007
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