arXiv subjects

Chao Bao

Publications and source records attributed to Chao Bao.

2 recordsLinked to original sources

arXiv2014

A note on the entropy of mean curvature flow

The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We will also prove that a smooth self-shrinker with low entropy is exact a hyperplane.

math.DG↗

arXiv2013

Gauss map of translating solitons of mean curvature flow

In this short note we study Bernstein's type theorem of translating solitons whose images of their Gauss maps are contained in compact subsets in an open hemisphere of the standard $\mathbf{S}^n$ (see Theorem 1.1). As a special case we get a classical Bernstein's type theorem in minimal submanifolds in $\mathbf{R}^{n+1}$ (see Corollary 1.2).

math.DG↗