2 citations · 3 across the 4 of their papers we have counts for
4 papers
Heat kernel Gaussian bounds on manifolds I: manifolds with non-negative Ricci curvature
Xiangjin Xu
This is first of series papers on new two-side Gaussian bounds for the heat kernel on a complete manifold . In this paper, on a complete manifold with $Ric(M)…
Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian
Xiangjin Xu
In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian , $$c_s λ\|u\|_{L^2(M)} \leq \| \partial_νu \…
Differential Harnack inequalities on Riemannian manifolds I : linear heat equation
Junfang Li, Xiangjin Xu
In the first part of this paper, we get new Li-Yau type gradient estimates for positive solutions of heat equation on Riemmannian manifolds with , .…
Gradient estimates for on manifolds and some Liouville-type theorems
Xiangjin Xu
In this paper, we first prove a localized Hamilton-type gradient estimate for the positive solutions of Porous Media type equations: with , on a complete…