Genus-one helicoids from a variational point of view

被引:0
作者
Hoffman, David [1 ]
White, Brian [1 ]
机构
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
关键词
Complete embedded minimal surface; helicoid; variational methods;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we use variational methods to prove existence of a complete, properly embedded, genus-one minimal surface that is asymptotic to a helicoid at infinity. We also prove some new properties of such helicoid-like Surfaces.
引用
收藏
页码:767 / 813
页数:47
相关论文
共 35 条
[1]  
[Anonymous], 1993, GLOBAL ANAL MODERN M
[2]  
[Anonymous], 1986, SURVEY MINIMAL SURFA
[3]   EMBEDDED MINIMAL-SURFACES WITH AN INFINITE NUMBER OF ENDS [J].
CALLAHAN, M ;
HOFFMAN, D ;
MEEKS, WH .
INVENTIONES MATHEMATICAE, 1989, 96 (03) :459-505
[4]   The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected [J].
Colding, TH ;
Minicozzi, WP .
ANNALS OF MATHEMATICS, 2004, 160 (02) :573-615
[5]   The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains [J].
Colding, TH ;
Minicozzi, WP .
ANNALS OF MATHEMATICS, 2004, 160 (02) :523-572
[6]   The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks [J].
Colding, TH ;
Minicozzi, WP .
ANNALS OF MATHEMATICS, 2004, 160 (01) :69-92
[7]   The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks [J].
Colding, TH ;
Minicozzi, WP .
ANNALS OF MATHEMATICS, 2004, 160 (01) :27-68
[8]   ON VALUES OF THE GAUSS MAP OF COMPLETE MINIMAL-SURFACES IN R3 [J].
EARP, RS ;
ROSENBERG, H .
COMMENTARII MATHEMATICI HELVETICI, 1988, 63 (04) :579-586
[9]   Minimal surfaces with helicoidal ends [J].
Ferrer, L ;
Martín, F .
MATHEMATISCHE ZEITSCHRIFT, 2005, 250 (04) :807-839