Showing 2025Show all
2 papers · 1 filter
math.AP2025
Gradient bounds for viscosity solutions to certain elliptic equations
Thalia Jeffres, Xiaolong Li
Our principal object of study is the modulus of continuity of a periodic or uniformly vanishing function \( u: \mathbb{R} ^{n} \rightarrow \mathbb{R} \) which satisfies a degenerat…
math.DG2025
Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem
Xiaolong Li
We prove that if a closed Riemannian manifold has finite fundamental group and satisfies the curvature condition \begin{equation*} R_{1313} +R_{1414} +R_{2323} + R_{2424}…