Negatively curved sets on surfaces of Constant Mean Curvature in ℝ3 are Large

Wu Hsiung Huang; Chun Chi Lin

doi:10.1007/s002050050074

Negatively curved sets on surfaces of Constant Mean Curvature in ℝ³ are Large

Wu Hsiung Huang, Chun Chi Lin

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	105-116
Number of pages	12
Journal	Archive for Rational Mechanics and Analysis
Volume	141
Issue number	2
DOIs	https://doi.org/10.1007/s002050050074
Publication status	Published - 1998 Mar 26
Externally published	Yes

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s002050050074

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abstract = "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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AB - 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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Negatively curved sets on surfaces of Constant Mean Curvature in ℝ³ are Large

Abstract

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