Existence of proper minimal surfaces of arbitrary topological type

被引：24

作者：

Ferrer, Leonor ^{[1
]}

Martin, Francisco ^{[1
]}

Meeks, William H., III ^{[2
]}

机构：

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

[2] Univ Massachusetts, Dept Math, Amherst, MA 01003 USA

来源：

ADVANCES IN MATHEMATICS | 2012年 / 231卷 / 01期

基金：

美国国家科学基金会;

关键词：

Complete bounded minimal surface; Proper minimal immersion; Calabi-Yau conjectures; CONVEX-BODIES; CONJECTURES; CURVATURE; BEHAVIOR; R-3;

D O I：

10.1016/j.aim.2012.05.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider a domain D in R-3 which is convex (possibly all R-3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f: M -> D. Moreover, if D is smooth and bounded, then we prove that the immersion f: M -> D can be chosen so that the limit sets of distinct ends of M arc disjoint connected compact sets in partial derivative D. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：378 / 413

页数：36

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