https://neckpinch.com/authors/guofang-wei/New arXiv papers by Guofang Wei, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2211.06403arxiv:2211.06403Fri, 11 Nov 2022 00:00:00 GMTGabriel Khan, Xuan Hien Nguyen, Malik Tuerkoen, Guofang Wei — We study the log-concavity of the first Dirichlet eigenfunction of the Laplacian for convex domains. For positively curved surfaces satisfying a condition involving the curvature and its second derivatives, we show that the first eigenfunction is strongly log-concave. Previously, for general convex domains, the log-concavity of the first eigenfunctions were only known when lying in ℝⁿ and Sⁿ. Using this estimate, we establish lower bounds on the fundamental gap of such regions. Furthermore, we study the behavior of these estimates under Ricci flow and other deformations of the metric.Ricci flowSurfacesEigenvalues & spectrum https://arxiv.org/abs/2203.05107arxiv:2203.05107Thu, 10 Mar 2022 00:00:00 GMTEric Chen, Guofang Wei, Rugang Ye — We employ the Ricci flow to derive a new theorem about Gromov almost flat manifolds, which generalizes and strengthens the celebrated Gromov–Ruh Theorem. In our theorem, the condition diam² |K| ≤ εₙ in the Gromov–Ruh Theorem is replaced by the substantially weaker condition \|Rm\|_(n/2) C_S² ≤ εₙ.Ricci flow