Bounded domains which are universal for minimal surfaces

被引:11
作者
Martin, Francisco [1 ]
Meeks, William H., III
Nadirashvili, Nikolai
机构
[1] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain
[2] Univ Massachusetts, Dept Math, Amherst, MA 01003 USA
[3] CNRS, LATP, CMI, F-13453 Marseille 13, France
基金
美国国家科学基金会;
关键词
D O I
10.1353/ajm.2007.0013
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We construct open domains in R-3 which do not admit complete properly immersed minimal surfaces with an annular end. These domains can not be smooth by a recent result of Martin and Morales.
引用
收藏
页码:455 / 461
页数:7
相关论文
共 13 条
[1]  
[Anonymous], 1986, SURVEY MINIMAL SURFA
[2]   ON THE RADIAL VARIATION OF BOUNDED ANALYTIC-FUNCTIONS ON THE DISC [J].
BOURGAIN, J .
DUKE MATHEMATICAL JOURNAL, 1993, 69 (03) :671-682
[3]  
COLDING TH, IN PRESS ANN MATH
[4]  
Collin P, 2004, J DIFFER GEOM, V67, P377
[5]  
CONWAY JB, 1995, GRAD TEXTS MATH, V159
[6]  
Farkas H.M., 1992, RIEMANN SURFACES, V71, P9, DOI [10.1007/978-1-4612-2034-3, DOI 10.1007/978-1-4612-2034-3]
[7]   On the asymptotic behavior of a complete bounded minimal surface in R3 [J].
Martín, F ;
Morales, S .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (10) :3985-3994
[8]  
Martín F, 2006, COMMENT MATH HELV, V81, P699
[9]  
Martín F, 2005, DUKE MATH J, V128, P559, DOI 10.1215/S0012-7094-04-12835-0
[10]   THE GEOMETRY AND CONFORMAL STRUCTURE OF PROPERLY EMBEDDED MINIMAL-SURFACES OF FINITE TOPOLOGY IN R(3) [J].
MEEKS, WH ;
ROSENBERG, H .
INVENTIONES MATHEMATICAE, 1993, 114 (03) :625-639