Contraction of Convex Hypersurfaces in $\mathbb R^3$ by Powers of Principal Curvatures
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.
math.AP↗