https://neckpinch.com/authors/kui-wang/New arXiv papers by Kui Wang, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1804.09806/arxiv:1804.09806Wed, 25 Apr 2018 00:00:00 GMTXiaolong Li, Kui Wang — This work is devoted to the study of parabolic frequency for solutions of the heat equation on Riemannian manifolds. We show that the parabolic frequency functional is almost increasing on compact manifolds with nonnegative sectional curvature, which generalizes a monotonicity result proved by C. Poon and by L. Ni. The proof is based on a generalization of R. Hamilton's matrix Harnack inequality for small time. As applications, we obtain a unique continuation result. Monotonicity of a new quantity under two-dimensional Ricci flow, closely related to the parabolic frequency functional, is derived as well.Ricci flowHarnack inequalitiesSurfaces https://neckpinch.com/papers/1603.05264/arxiv:1603.05264Wed, 16 Mar 2016 00:00:00 GMTXiaolong Li, Lei Ni, Kui Wang — We show that a four-dimensional complete gradient shrinking Ricci soliton with positive isotropic curvature is either a quotient of S^4 or a quotient of S^3 cross R. This gives a clean classification result removing the earlier additional assumptions in [13] by Wallach and the second author.Ricci solitons4-manifoldsSphere theorems