https://neckpinch.com/authors/guanhua-shao/New arXiv papers by Guanhua Shao, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2609.10197/arxiv:2609.10197Wed, 09 Sep 2026 00:00:00 GMTAprameya Girish Hebbar, Guanhua Shao, Qi Sun — We show that on any closed orientable real-analytic Riemannian surface, any smoothly immersed closed immortal curve-shortening flow converges to a unique non-constant closed geodesic.Curve shorteningLong-time existence & convergence https://neckpinch.com/papers/2507.19428/arxiv:2507.19428Fri, 25 Jul 2025 00:00:00 GMTGuanhua Shao, Jiahua Zou — For a general class of cones in ℝ³, we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mean curvature flow with genus strictly decreasing but not to zero at the first singular time. We also construct a sequence of self-expanders with unbounded genus which are asymptotic to the same rotationally symmetric cone. Moreover, we characterize the asymptotic behavior of the sequence.Mean curvature flowSelf-shrinkers & translatorsWeak & singular flowsRotational symmetry & warped products