On the manifold of closed hypersurfaces in $\mathbb{R}^n$

Jan Prüss; Gieri Simonett

doi:10.3934/dcds.2013.33.5407

Article Contents

2013, Volume 33, Issue 11&12: 5407-5428. Doi: 10.3934/dcds.2013.33.5407

This issue Previous Article Singular limits for the two-phase Stefan problem Next Article Integration with vector valued measures

On the manifold of closed hypersurfaces in $\mathbb{R}^n$

Jan Prüss^1, and
Gieri Simonett^2,

1.
Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, D-60120 Halle
2.
Department of Mathematics, Vanderbilt University, Nashville, TN 37240

Received: July 31, 2011

Revised: November 30, 2011

Published: October 2013

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Abstract

Several results from differential geometry of hypersurfaces in $\mathbb{R}^n$ are derived to form a tool box for the direct mapping method. The latter technique has been widely employed to solve problems with moving interfaces, and to study the asymptotics of the induced semiflows.

Keywords:

Principal curvature,
mean curvature,
surface gradient and surface divergence,
normal variation,
tubular neighborhood,
level function,
approximation of hypersurfaces.

Mathematics Subject Classification: Primary: 35R37; Secondary: 53C44.

Citation:

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References

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