SOME STRUCTURE THEOREMS FOR COMPLETE CONSTANT MEAN-CURVATURE SURFACES WITH BOUNDARY A CONVEX CURVE

被引：2

作者：

EARP, RS ^{[1
]}

ROSENBERG, H ^{[1
]}

机构：

[1] UNIV PARIS 07,DEPT MATH,F-75251 PARIS,FRANCE

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1991年 / 113卷 / 04期

关键词：

CONSTANT MEAN CURVATURE; DELAUNAY SURFACE; ALEXANDROV REFLECTION PRINCIPLE;

D O I：

10.2307/2048783

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be a properly embedded, connected, complete surface in R3 with non-zero constant mean curvature and with boundary a strictly convex plane curve C. It is shown that if M is contained in a vertical cylinder of R+3, outside of some compact set of R3, and if M is contained in a half-space of R3 determined by C, then M inherits the symmetries of C. In particular, M is a Delaunay surface if C is a circle. It is also shown that if M has a finite number of vertical annular ends and the area of the flat disc D bounded by C is not "too small," then M lies in a half-space.

引用

页码：1045 / 1053

页数：9