A representation formula for the inverse harmonic mean curvature flow

Knut Smoczyk
2005 Elemente der Mathematik  
Let M t be a smooth family of embedded, strictly convex hypersurfaces in R n+1 evolving by the inverse harmonic mean curvature flow 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.
doi:10.4171/em/9 fatcat:ir2v34phjja3palxinoi3rcmtq