A representation formula for the inverse harmonic mean curvature flow

Knut Smoczyk

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Submission date: 07. Oct. 2003
Pages: 12
published in: Elemente der Mathematik, 60 (2005) 2, p. 57-65 
DOI number (of the published article): 10.4171/EM/9
Bibtex
MSC-Numbers: 53C44
Keywords and phrases: mean curvature flow, harmonic mean curvature flow, representation formula
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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.