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MiS Preprint
85/2003

A representation formula for the inverse harmonic mean curvature flow

Knut Smoczyk

Abstract

Let $M_t$ be a smooth family of embedded, strictly convex hypersurfaces in $\mathbb R^{n+1}$ evolving by the inverse harmonic mean curvature flow $$\frac{d}{dt} F=\mathcal H^{-1}\nu.$$ Surprisingly, we can determine the explicit solution of this nonlinear parabolic equation with some Fourier analysis. More precisely, there exists a representation formula for the evolving hypersurfaces $M_t$ that can be expressed in terms of the heat kernel on $S^n$ and the initial support function.

Received:
Oct 7, 2003
Published:
Oct 7, 2003
MSC Codes:
53C44
Keywords:
mean curvature flow, harmonic mean curvature flow, representation formula

Related publications

inJournal
2005 Repository Open Access
Knut Smoczyk

A representation formula for the inverse harmonic mean curvature flow

In: Elemente der Mathematik, 60 (2005) 2, pp. 57-65