On the generalized Weyl problem for flat metrics in the hyperbolic 3-space

被引：2

作者：

Galvez, Jose A. ^{[1
]}

Martinez, Antonio ^{[1
]}

Teruel, Jose L. ^{[1
]}

机构：

[1] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 410卷 / 01期

关键词：

Weyl's problem; Complete flat surfaces; Isolated singularities; Hyperbolic; 3-space; ISOLATED SINGULARITIES; CAUCHY-PROBLEM; SURFACES; CURVATURE; FRONTS; SPACE;

D O I：

10.1016/j.jmaa.2013.08.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with the study of complete embedded flat surfaces in H-3 with a finite number of isolated singularities. We give a detailed information about its topology, conformal type and metric properties. We show how to solve the generalized Weyl's problem of realizing isometrically any complete flat metric with Euclidean singularities in H-3 which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：144 / 150

页数：7

共 20 条

[1] The Cauchy problem for improper affine spheres and the Hessian one equation [J].

Aledo, Juan A. ;

Chaves, Rosa M. B. ;

Galvez, Jose A. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (09) :4183-4208

[2] The affine Cauchy problem [J].

Aledo, Juan A. ;

Martinez, Antonio ;

Milan, Francisco .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 351 (01) :70-83

[3]

ALEXANDROV AD, 2006, SELECTED WORKS 2

[4] Complete flat surfaces with two isolated singularities in hyperbolic 3-space [J].

Corro, Armando V. ;

Martinez, Antonio ;

Milan, Francisco .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 366 (02) :582-592

[5] ON A CLASS OF CONFORMAL METRICS WITH APPLICATION TO DIFFERENTIAL GEOMETRY IN LARGE [J].

FINN, R .

COMMENTARII MATHEMATICI HELVETICI, 1965, 40 (01) :1-&

[6] Embedded isolated singularities of flat surfaces in hyperbolic 3-space [J].

Gálvez, JA ;

Mira, P .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2005, 24 (02) :239-260

[7] Flat surfaces in the hyperbolic 3-space [J].

Gálvez, JA ;

Martínez, A ;

Milán, F .

MATHEMATISCHE ANNALEN, 2000, 316 (03) :419-435

[8]

Heijenoort J.V., 1952, COMMUNICATION PURE A, V5, P223

[9] VOLLSTANDIGE KONFORME METRIKEN UND ISOLIERTE SINGULARITATEN SUBHARMONISCHER FUNKTIONEN [J].

HUBER, A .

COMMENTARII MATHEMATICI HELVETICI, 1966, 41 (02) :105-&

[10]

Huber A., 1960, COMMENT MATH HELV, V34, P99

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