3 papers
math.DG2026
Uniqueness of the asymptotic limits for Ricci-flat manifolds with linear volume growth II
Zetian Yan, Xingyu Zhu
We relate the uniqueness of asymptotic limits for noncollapsed Ricci flat manifolds with linear volume growth to the existence of a harmonic function asymptotic to a Busemann funct…
math.DG2025
Uniqueness of the asymptotic limits for Ricci-flat manifolds with linear volume growth
Zetian Yan, Xingyu Zhu
Under natural assumptions on curvature and cross section, we establish the uniqueness of asymptotic limits and the exponential convergence rate for complete noncollapsed Ricci-flat…
math.DG2024
On the topology of manifolds with nonnegative Ricci curvature and linear volume growth
Dimitri Navarro, Jiayin Pan, Xingyu Zhu
Understanding the relationships between geometry and topology is a central theme in Riemannian geometry. We establish two results on the fundamental groups of open (complete and no…