On the nonexistence of a hypersurface of prescribed mean curvature with a given boundary

Robert D Gulliver

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A general method is developed for finding necessary conditions for a given codimension-two submanifold Γ of a riemannian manifold to be the boundary of an immersed hypersurface of prescribed mean curvature. In the simplest case the condition is a comparison of the magnitude of the mean curvature with the ratio of the volume of the projection of Γ into a hyperplane to the volume of the interior of that projection. The method is applied to show that certain recent existence results for surfaces of prescribed mean curvature may not be quantitatively improved.

Original languageEnglish (US)
Pages (from-to)15-39
Number of pages25
JournalManuscripta Mathematica
Volume11
Issue number1
DOIs
StatePublished - Mar 1 1974

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