Deformation and stability of surfaces with constant mean curvature

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14 Citations (Scopus)

Abstract

For a CMC immersion from a two-dimensional compact smooth manifold with boundary into the Euclidean three-space, we give sufficient conditions under which it has a CMC deformation fixing the boundary. Moreover, we give a criterion of the stability for CMC immersions. Both of these are achieved by using the properties of eigenvalues and eigenfunctions of an eigenvalue problem associated to the second variation of the area functional. In a certain special case, by combining these results, we obtain a ‘visible’ way of judging the stability.

Original languageEnglish
Pages (from-to)145-159
Number of pages15
JournalTohoku Mathematical Journal
Volume54
Issue number1
DOIs
Publication statusPublished - Jan 1 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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