https://neckpinch.com/authors/junfang-li/New arXiv papers by Junfang Li, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.35394arxiv:2610.35394Mon, 26 Oct 2026 00:00:00 GMTJunfang Li — We extend the quermassintegral inequalities of our earlier work from star-shaped domains to a substantially broader class of domains in Euclidean space, which we call spiral-star-shaped. A smooth domain is spiral-star-shaped if its boundary satisfies ⟨ X+A X,ν⟩>0 for some fixed skew-symmetric linear map A, where X is the position vector and ν is the outward unit normal. The vector field X+A X is conformal Killing, with dilation component X and rotational component A X; its trajectories combine expansion and rotation, giving rise to the spiral terminology. When A=0, it reduces to ordinary star-shapedness, while nonzero A allows domains that are not star-shaped in the usual radial sense. For smooth k-convex spiral-star-shaped domains, we prove long-time existence and exponential convergence to a round sphere for a locally constrained inverse curvature flow. The positive spiral support function provides the geometric control needed to treat initial hypersurfaces that need not be star-shaped in the usual sense. Monotonicity of the quermassintegrals along the flow yields sharp quermassintegral inequalities in this enlarged class, with equality if and only if the domain is a ball.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsLong-time existence & convergenceGeometric inequalities