3 papers
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.DG2024
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…