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：
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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.
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页码：105 / 116
页数：11
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