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

Wu Hsiung Huang, Chun Chi Lin

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6 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 languageEnglish
Pages (from-to)105-116
Number of pages12
JournalArchive for Rational Mechanics and Analysis
Volume141
Issue number2
DOIs
Publication statusPublished - 1998 Mar 26

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ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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