https://neckpinch.com/authors/hejun-wang/New arXiv papers by Hejun Wang, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2104.05966/arxiv:2104.05966Tue, 13 Apr 2021 00:00:00 GMTYusha Lv, Hejun Wang — In this paper, we study a class of fully nonlinear contracting curvature flows of closed, uniformly convex hypersurfaces in the Euclidean space ℝⁿ⁺¹ with the normal speed Φ given by r^αF^β or u^αF^β, where F is a monotone, symmetric, inverse-concave, homogeneous of degree one function of the principal curvatures, r is the distance from the hypersurface to the origin and u is the support function of hypersurface. If α≥ β+1 when Φ=r^αF^β or α> β+1 when Φ=u^αF^β, we prove that the flow exists for all times and converges to the origin. After proper rescaling, we prove that the normalized flow converges exponentially in the C^∞ topology to a sphere centered at the origin. Furthermore, for special inverse concave curvature function F=K^(s/n)F₁^(1-s)(s∈(0, 1]), where K is Gauss curvature and F₁ is inverse-concave, we obtain the asymptotic convergence for the flow with Φ=u^αF^β when α=β+1. If α<β+1, a counterexample is given for the above convergence when speed equals to r^αF^β.Other curvature flowsHomogeneous spacesLong-time existence & convergence