- Xiaolong Li
- Wichita State University
- Date: Apr. 30, Wednesday, 2025
- Time: 12:00pm -- 12:50pm
- Host: Yuming Paul Zhang
- Room: Parker 328
- Abstract: In this talk, I will discuss the modulus of continuity estimates for quasilinear and fully nonlinear parabolic equations: the moduli of continuity of solutions to parabolic equations are sub-solutions of suitable equations of one space variable. Then I will discuss two main applications: sharp time-interior gradient estimates and lower bounds of the first nonzero eigenvalue of the Laplacian and p-Laplacian on manifolds. The talk is based on several works, some of which are joint work with Dr. Kui Wang at Soochow University.