Contraction of Convex Hypersurfaces in R3 by Powers of Principal Curvatures
Abstract
We study the contraction of strictly convex, axially symmetric hypersurfaces by a non-symmetric, non-homogeneous, fully nonlinear function of curvature. Starting from axially symmetric hypersurfaces with even profile curves, we show evolving hypersurfaces converge to a point in a finite time, and under proper rescaling, solutions will converge to a convex hypersurface.
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