Negatively Curved Sets on Surfaces of Constant Mean Curvature in ℝ3 are Large

被引：0

作者：

Wu-Hsiung Huang

Chun-Chi Lin

机构：

[1] Department of Mathematics,

[2] National Taiwan University,undefined

[3] Taipei,undefined

[4] Taiwan,undefined

[5] Department of Mathematics,undefined

[6] Rice University,undefined

[7] Houston,undefined

[8] TX 77251,undefined

[9] USA,undefined

来源：

Archive for Rational Mechanics and Analysis | 1998年 / 141卷

关键词：

Differential Equation; Partial Differential Equation; Elliptic Partial Differential Equation; Convexity Result; Extremal Domain;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

It is proved that the negatively curved set M− on a nonparametric surface M of constant mean curvature in ℝ3 must extend to the boundary ∂M, if M− is nonempty. For M parametric, if M− is compactly included in the interior of M, then M− is at least as large as an extremal domain. The results imply certain convexity results on elliptic partial differential equations. Second‐order calculus of variation is employed.

引用

页码：105 / 116

页数：11

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