3 citations · 3 across the 7 of their papers we have counts for
7 papers
Integral of Scalar Curvature: Sharp Asymptotic Bounds and Rigidity
Guoyi Xu
For any complete noncompact manifolds of nonnegative sectional curvature, with , we obtain $\displaystyle \lim_{r\to\infty}r^{2-n}\int_{B_p(r)}\Sc_g\,dV_g\le…
Integral of Scalar Curvature under Volume Collapse
Guoyi Xu
We construct a smooth complete metric on with strictly positive Ricci curvature and $\displaystyle \lim_{s\rightarrow\infty}s^{-1}\int_{B_p(s)}\Sc\ddμ= \infty$. This gives a…
A Harmonic-Map Proof of Mostow Rigidity
Guoyi Xu
Given an isomorphism between the fundamental groups of two compact hyperbolic manifolds of dimension at least three, we consider the associated equivariant harmonic lift. We establ…
Integrals and Rigidity on Manifolds with Nonnegative Ricci Curvature
Zixuan Chen, Guoyi Xu, Shuai Zhang
We prove the general sharp mean value inequality for non-negative superharmonic functions and its corresponding rigidity, which removes the radius restriction of Schoen-Yau's class…
The sharp diameter bound of stable minimal surfaces
Qixuan Hu, Guoyi Xu, Shuai Zhang
For three dimensional complete Riemannian manifolds with scalar curvature no less than one, we obtain the sharp upper bound of complete stable minimal surfaces' diameter.
Volume growth and positive scalar curvature
Guodong Wei, Guoyi Xu, Shuai Zhang
For three dimensional complete, non-compact Riemannian manifolds with non-negative Ricci curvature and uniformly positive scalar curvature, we obtain the sharp linear volume growth…
Extrinsic Bonnet-Myers Theorem and almost rigidity
Weiying Li, Guoyi Xu
We establish the extrinsic Bonnet-Myers Theorem for compact Riemannian manifolds with positive Ricci curvature. And we show the almost rigidity for compact hypersurfaces, which hav…