TITLE

A homotopy approach to solving the inverse mean curvature flow

AUTHOR(S)
Hein, Bernhard
PUB. DATE
February 2007
SOURCE
Calculus of Variations & Partial Differential Equations;Feb2007, Vol. 28 Issue 2, p249
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In $$\mathbb{R}^{n}$$ , n < 7, we treat the quasilinear, degenerate parabolic initial and boundary value problem which is the natural parabolic extension of Huisken and Ilmanen’s weak inverse mean curvature flow (IMCF). We prove long time existence and partial uniqueness of Lipschitz continuous weak solutions u( x, t) and show C 1,α-regularity for the sets ∂{ x| u( x, t) < z }. Our approach offers a new approximation for weak solutions of the IMCF starting from a class of interesting and easily obtainable initial values; for these, the above sets are shown to converge against corresponding surfaces of the IMCF as t → ∞ globally in Hausdorff distance and locally uniformly with respect to the C 1,α-norm.
ACCESSION #
23218186

 

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