18 citations · 42 across the 16 of their papers we have counts for
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Integral of scalar curvature on manifolds with a pole
Guoyi Xu
On any complete three dimensional Riemannian manifold with a pole and non-negative Ricci curvature, we show that the asymptotic scaling invariant integral of scalar curvature, is e…
The construction of -splitting map
Guoyi Xu, Jie Zhou
For a geodesic ball with non-negative Ricci curvature and almost maximal volume, without using compactness argument, we construct an -splitting map on a concentric geodesic ball…
The rigidity and stability of gradient estimates
Qixuan Hu, Guoyi Xu, Chengjie Yu
In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sh…
The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls
Haibin Wang, Guoyi Xu, Jie Zhou
On complete noncompact Riemannian manifolds with non-negative Ricci curvature, Li-Schoen proved the uniform Poincare inequality for any ge odesic ball. In this note, we obtain the…
The growth rate of harmonic functions
Guoyi Xu
We study the growth rate of harmonic functions in two aspects: gradient estimate and frequency. We obtain the sharp gradient estimate of positive harmonic function in geodesic ball…
Local estimate of fundamental groups
Guoyi Xu
For any complete -dim Riemannian manifold with nonnegative Ricci curvature, Kapovitch and Wilking proved that any finitely generated subgroup of the fundamental group $π_1…
Integral of scalar curvature on non-parabolic manifolds
Guoyi Xu
Using the monotonicity formulas of Colding and Minicozzi, we prove that on any complete, non-parabolic Riemannian manifold with non-negative Ricci curvature, the asympto…
The (p;m)-width of Riemannian manifolds and its realization
Guoyi Xu
While studying the existence of closed geodesics and minimal hypersurfaces in compact manifolds, the concept of width was introduced in different contexts. Generally, the width is…
Three circles theorems for harmonic functions
Guoyi Xu
We proved two Three Circles Theorems for harmonic functions on manifolds in integral sense. As one application, on manifold with nonnegative Ricci curvature, whose tangent cone at…
Large time behavior of the heat kernel
Guoyi Xu
In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional max…
An equation linking -entropy with reduced volume
Guoyi Xu
-entropy and reduced volume for the Ricci flow were introduced by Perelman, which had proved their importance in the study of the Ricci flow. L. Ni studied the analogo…
Lower bound of Ricci flow's existence time
Guoyi Xu
Let be a compact -dim () manifold with nonnegative Ricci curvature, and if we assume that has nonnegative isotropic cur…
The short time asymptotics of Nash entropy
Guoyi Xu
Let be a complete Riemannian manifold with , is the heat kernel on , and . Nash entropy is defined as $N(H,…
Local pinching estimates in 3-dim Ricci flow
Bing-Long Chen, Guoyi Xu, Zhuhong Zhang
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions whic…
Short-time existence of the Ricci flow on noncompact Riemannian manifolds
Guoyi Xu
In this paper, we give the first detailed proof of the short-time existence of Deane Yang's local Ricci flow. Then using the local Ricci flow, we prove short-time existence of the…
Examples of hypersurfaces flowing by curvature in a Riemannian manifold
Robert Gulliver, Guoyi Xu
This paper gives some examples of hypersurfaces evolving in time with speed determined by functions of the normal curvatures in an -dimensional hyperbolic manifol…