Complete Non-Orientable Minimal Surfaces in ℝ³and Asymptotic Behavior

• Autorzy: Antonio Alarcón , Francisco J. López
• 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

Słowa kluczowe

EN

Complete minimal surfaces; non-orientable surfaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2013-12-02

zaakceptowano

2014-06-17

online

2014-07-26

Twórcy

autor

Antonio Alarcón

• Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain

autor

Francisco J. López

• Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain

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.

Identyfikatory

DOI

10.2478/agms-2014-0007