2 citations · 4 across the 7 of their papers we have counts for
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Stability and singular set of the two-convex level set flow
Siao-Hao Guo
The level set flow of a mean-convex closed hypersurface is stable off singularities, in the sense that the level set flow of the perturbed hypersurface would be close in the smooth…
Singular set and curvature blow-up rate of the level set flow
Siao-Hao Guo
Under certain conditions such as the -convexity, a singularity of the level set flow is of type I (in the sense that the rate of curvature blow-up is constrained before and afte…
Asymptotic Behavior and Stability of Mean Curvature Flow with a Conical End
Siao-Hao Guo
If the initial hypersurface of an immortal mean curvature flow is asymptotic to a regular cone whose entropy is small, the flow will become asymptotically self-expanding. Moreover,…
Extension of two-dimensional mean curvature flow with free boundary
Siao-Hao Guo
Given a mean curvature flow of compact, embedded surfaces satisfying Neumann free boundary condition on a mean convex, smooth support surface in 3-dimensional Euclidean space…
Analysis of Velzquez's solution to the mean curvature flow with a type singularity
Siao-Hao Guo, Natasa Sesum
J.J.L. Velzquez in 1994 used the degree theory to show that there is a perturbation of Simons' cone, starting from which the mean curvature flow develops a type $\mathrm…
Existence of self-shrinkers to the degree-one curvature flow with a rotationally symmetric conical end
Siao-Hao Guo
Given a smooth, symmetric, homogeneous of degree one function satisfying for all , and a rotationally symmetr…
Uniqueness of self-shrinkers to the degree-one curvature flow with a tangent cone at infinity
Siao-Hao Guo
Given a smooth, symmetric, homogeneous of degree one function satisfying for all , and an oriented, proper…