35 citations · 258 across the 39 of their papers we have counts for
39 papers
Decomposition of global solutions of bi-laplacian Nonautonomous Schrödinger equations
Avy Soffer, Jiayan Wu, Xiaoxu Wu +1
We study the bi-Laplacian Schrödinger equation with a general interaction term, which may be linear or nonlinear and is allowed to be time-dependent. We show that global solutions…
Diameter estimates for submanifolds in manifolds with nonnegative curvature
Jia-Yong Wu
Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the sub…
Shrinkers with curvature pinching conditions are compact
Guoqiang Wu, Jia-Yong Wu
In this paper, we give various curvature pinching conditions such that shrinkers are compact. On one hand, we prove that shrinkers with positive Ricci curvature are compact when th…
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…
Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition
Xuenan Fu, Jia-Yong Wu
In this paper, we prove Souplet-Zhang type gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with the compact boundary under the Dirichlet bound…
Gap theorems for ends of smooth metric measure spaces
Bobo Hua, Jia-Yong Wu
In this paper, we establish two gap theorems for ends of smooth metric measure space with the Bakry-Émery Ricci tensor in a geodesic b…
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…
Geometric inequalities and rigidity of gradient shrinking Ricci solitons
Jia-Yong Wu
In this paper we prove that the Sobolev inequality, the logarithmic Sobolev inequality, the Schrödinger heat kernel upper bound, the Faber-Krahn inequality, the Nash inequality and…
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…
Sharp Gaussian upper bounds for Schrödinger heat kernel on gradient shrinking Ricci solitons
Jia-Yong Wu
On gradient shrinking Ricci solitons, we observe that the study of Schrödinger heat kernel seems to be more natural than the classical heat kernel. In this paper we derive sharp Ga…
Time analyticity for heat equation on gradient shrinking Ricci solitons
Jia-Yong Wu
On a complete non-compact gradient shrinking Ricci soliton, we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the spac…
Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons
Jia-Yong Wu, Peng Wu
In this paper, we study harmonic and caloric functions of polynomial growth on a complete non-compact gradient shrinking Ricci soliton. On one hand, when the scalar curvature satis…
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…
Gradient estimates for a nonlinear parabolic equation and Liouville theorems
Jia-Yong Wu
We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we d…
Rigidity of closed metric measure spaces with nonnegative curvature
Jia-Yong Wu
We show that one-dimensional circle is the only case for closed smooth metric measure spaces with nonnegative Bakry-Émery Ricci curvature whose spectrum of the weighted Laplacian h…
Myers' type theorem with the Bakry-Émery Ricci tensor
Jia-Yong Wu
In this paper we prove a new Myers' type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry-Émery Ricci tensor ha…
Comparison geometry for integral Bakry-Émery Ricci tensor bounds
Jia-Yong Wu
We prove mean curvature and volume comparison estimates on smooth metric measure spaces when their integral Bakry-Émery Ricci tensor bounds, extending Wei-Wylie's comparison result…
Liouville property for -harmonic functions with polynomial growth
Jia-Yong Wu
We prove a Liouville property for any -harmonic function with polynomial growth on a complete noncompact smooth metric measure space when the Bakry-Émery Ricci…
Elliptic gradient estimates for a nonlinear heat equation and applications
Jia-Yong Wu
In this paper, we study elliptic gradient estimates for a nonlinear -heat equation, which is related to the gradient Ricci soliton and the weighted log-Sobolev constant of smoot…
On -Liouville property for smooth metric measure spaces
Jia-Yong Wu, Peng Wu
In this short paper we study -Liouville property with for nonnegative -subharmonic functions on a complete noncompact smooth metric measure space …
Gradient shrinking Ricci solitons of half harmonic Weyl curvature
Jia-Yong Wu, Peng Wu, William Wylie
We prove that a four-dimensional gradient shrinking Ricci soliton with is either Einstein, or a finite quotient of , or $\…
Heat kernel on smooth metric measure spaces and applications
Jia-Yong Wu, Peng Wu
We derive a Harnack inequality for positive solutions of the -heat equation and Gaussian upper and lower bounds for the -heat kernel on complete smooth metric measure spaces…