Geometry and stability of bubbles with gravity

Miyuki Koiso, Bennett Palmer

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We study the variational theory of surfaces whose mean curvature is prescribed to be a linear function of their height above a horizontal plane (PMC surfaces). We develop a flux formula and use it to prove nonexistence results for closed PMC surfaces. The perturbation theory for PMC surfaces is studied. We obtain necessary conditions for the stability of PMC surfaces with planar boundaries. A height estimate is obtained for stable PMC graphs.

Original languageEnglish
Pages (from-to)65-98
Number of pages34
JournalIndiana University Mathematics Journal
Volume54
Issue number1
DOIs
Publication statusPublished - Apr 28 2005
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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