works on
fundamental groups 1gradient estimates 1harmonic maps 1hyperbolic manifolds 1mostow rigidity 1

From the 1 of 4 linked papers with an AI index.

collaborators

4 papers

math.DG2026

A Harmonic-Map Proof of Mostow Rigidity

Guoyi Xu

The paper proves Mostow rigidity for compact hyperbolic manifolds of dimension ≥3 by establishing a sharp pointwise gradient estimate for an equivariant harmonic lift associated to…

math.DG2026

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…

math.DG2025

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.

math.DG2025

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…