HOLOMORPHIC QUADRATIC DIFFERENTIALS AND THE BERNSTEIN PROBLEM IN HEISENBERG SPACE

被引：25

作者：

Fernandez, Isabel ^{[1
]}

Mira, Pablo ^{[2
]}

机构：

[1] Univ Seville, Dept Matemat Aplicada 1, E-41012 Seville, Spain

[2] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, E-30203 Murcia, Spain

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 11期

关键词：

Minimal graphs; Bernstein problem; holomorphic quadratic differential; Heisenberg group; MEAN-CURVATURE SURFACES; H-2 X R; MINIMAL-SURFACES; HARMONIC MAPS;

D O I：

10.1090/S0002-9947-09-04645-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify the entire minimal vertical graphs in the Heisenberg group Nil(3) endowed with a Riemannian left-invariant metric This classification, which provides It Solution to the Bernstein problem in Nil(3), is given in terms of the Abresch-Rosenberg holomorphic differential for minimal surfaces in Nil(3).

引用

页码：5737 / 5752

页数：16

共 24 条

[1] A Hopf differential for constant mean curvature surfaces in S2 x R and H2 x R [J].

Abresch, U ;

Rosenberg, H .

ACTA MATHEMATICA, 2004, 193 (02) :141-174

[2]

Abresch U., 2005, Mat. Contemp., V28, P1

[3] The Dirichlet problem for constant mean curvature surfaces in Heisenberg space [J].

Alias, Luis J. ;

Dajczer, Marcos ;

Rosenberg, Harold .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2007, 30 (04) :513-522

[4]

BARONE V, 2007, CALC VAR PARTIAL DIF, V30, P17

[5]

BRYANT RL, 1987, ASTERISQUE, P321

[6]

Cheng JH, 2005, ANN SCUOLA NORM-SCI, V4, P129

[7] MAXIMAL SPACE-LIKE HYPERSURFACES IN LORENTZ-MINKOWSKI SPACES [J].

CHENG, SY ;

YAU, ST .

ANNALS OF MATHEMATICS, 1976, 104 (03) :407-419

[8]

COLLIN P, 2007, CONSTRUCTION HARMONI

[9]

DANIEL B, 2007, HALF SPACE THEOREM E

[10]

DANIEL B, 2006, GAUSS MAP MINIMAL SU

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