Complete minimal discs in Hadamard manifolds

被引：2

作者：

Ripoll, Jaime ^{[1
]}

Tomi, Friedrich ^{[2
]}

机构：

[1] Univ Fed Rio Grande do Sul, Inst Matemat, Av Bento Goncalves 9500, BR-91540000 Porto Alegre, RS, Brazil

[2] Heidelberg Univ, Math Inst, Neuhenheimer Feld 288, D-69120 Heidelberg, Germany

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2017年 / 10卷 / 04期

关键词：

Minimal discs; Hadamard manifolds; asymptotic boundary; ASYMPTOTIC DIRICHLET PROBLEMS; HYPERBOLIC SPACE; REGULARITY; CURVATURE;

D O I：

10.1515/acv-2015-0044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the classical approach we show the existence of disc type solutions to the asymptotic Plateau problem in certain Hadamard manifolds which may have arbitrarily strong curvature and volume growth.

引用

页码：315 / 330

页数：16

共 23 条

[1] COMPLETE MINIMAL HYPERSURFACES IN HYPERBOLIC N-MANIFOLDS [J].

ANDERSON, MT .

COMMENTARII MATHEMATICI HELVETICI, 1983, 58 (02) :264-290

[2] COMPLETE MINIMAL VARIETIES IN HYPERBOLIC SPACE [J].

ANDERSON, MT .

INVENTIONES MATHEMATICAE, 1982, 69 (03) :477-494

[3]

[Anonymous], 1966, GRUNDLEHREN MATH WIS

[4] Trapping quasiminimizing submanifolds in spaces of negative curvature [J].

Bangert, V ;

Lang, U .

COMMENTARII MATHEMATICI HELVETICI, 1996, 71 (01) :122-143

[5]

Casteras J., 2015, PREPRINT

[6] ASYMPTOTIC DIRICHLET PROBLEMS FOR HARMONIC-FUNCTIONS ON RIEMANNIAN-MANIFOLDS [J].

CHOI, HI .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 281 (02) :691-716

[7]

Coskunuzer B., 2010, PREPRINT

[8]

Coskunuzer B, 2015, PREPRINT

[9]

Dajczer M., 2013, PREPRINT

[10]

Dierkes U, 2010, GRUNDLEHR MATH WISS, V340, P1, DOI 10.1007/978-3-642-11700-8

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