9 papers
Counting ends on shrinkers
Jia-Yong Wu
In this paper we apply a geometric covering method to study the number of ends on shrinkers. On one hand, we prove that the number of ends on any complete non-compact shrinker is a…
Sharp gradient estimates on weighted manifolds with compact boundary
Ha Tuan Dung, Nguyen Thac Dung, Jia-Yong Wu
In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we p…
Gradient estimates for weighted harmonic function with Dirichlet boundary condition
Nguyen Thac Dung, Jia-Yong Wu
We prove a Yau's type gradient estimate for positive -harmonic functions with the Dirichlet boundary condition on smooth metric measure spaces with compact boundary when the inf…
Comparison geometry for integral radial Bakry-Émery Ricci tensor bounds
Jia-Yong Wu
In this paper we prove mean curvature comparisons and volume comparisons on a smooth metric measure space when the integral radial Bakry-Émery Ricci tensor and the potential functi…
Sharp upper diameter bounds for compact shrinking Ricci solitons
Jia-Yong Wu
We give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman's entropy functional. The sharp cases could oc…
New differential Harnack inequalities for nonlinear heat equations
Jia-Yong Wu
We prove constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation on closed manifolds. We also derive a new interpolat…