35 citations · 91 across the 12 of their papers we have counts for
12 papers
The characterizations on a class of weakly weighted Einstein-Finsler metrics
Xinyue Cheng, Hong Cheng, Pengsheng Wu
In this paper, we study the weakly weighted Einstein-Finsler metrics. First, we show that weakly weighted Einstein-Kropina metrics must be of isotropic S-curvature with respect to…
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…
Curvature decompositions on Einstein four-manifolds
Peng Wu
For Einstein four-manifolds with positive scalar curvature, we derive relations among various positivity conditions on the curvature tensor, some of which are of great importance i…
Einstein four-manifolds with self-dual Weyl curvature of nonnegative determinant
Peng Wu
We prove that simply connected Einstein four-manifolds of positive scalar curvature are conformally Kähler if and only if the determinant of the self-dual Weyl curvature is positiv…
Berger curvature decomposition, Weitzenböck formula, and canonical metrics on four-manifolds
Peng Wu
We first provide an alternative proof of the classical Weitzneböck formula for Einstein four-manifolds using Berger curvature decomposition, motivated by which we establish a unifi…
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…
Heat Kernel on Smooth Metric Measure Spaces with Nonnegative Curvature
Jia-Yong Wu, Peng Wu
We derive a local Gaussian upper bound for the -heat kernel on complete smooth metric measure space with nonnegative Bakry-Émery Ricci curvature, which generali…
A generalization of the Cai--Galloway splitting theorem to smooth metric measure spaces
Jeffrey S. Case, Peng Wu
We generalize the splitting theorem of Cai-Galloway for complete Riemannian manifolds with $\Ric\geq-(n-1)$ admitting a family of compact hypersurfaces tending to infinity with mea…
On Volume Growth of Gradient Steady Ricci Solitons
Guofang Wei, Peng Wu
In this paper we study volume growth of gradient steady Ricci solitons. We show that if the potential function satisfies a uniform condition, then the soliton has at most Euclidean…
On Potential Function of Gradient Steady Ricci Solitons
Peng Wu
In this paper we study potential function of gradient steady Ricci solitons. We prove that infimum of potential function decays linearly; in particular, potential function of recti…