Contraction of Convex Hypersurfaces in $\mathbb R^3$ by Powers of Principal Curvatures

Meraj Hosseini

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arXiv · 2409.18381

Contraction of Convex Hypersurfaces in $\mathbb R^3$ by Powers of Principal Curvatures

Meraj Hosseini

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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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Meraj Hosseini. 2024-09-27. Contraction of Convex Hypersurfaces in $\mathbb R^3$ by Powers of Principal Curvatures. https://arxiv.org/abs/2409.18381

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