arXiv subjects

Huihong Jiang

Publications and source records attributed to Huihong Jiang.

3 recordsLinked to original sources

arXiv2025

Examples of open manifolds with almost quadratic volume growth and infinite Betti numbers

We construct a family of examples of complete $(2+n)-$dimensional ($n\ge 2$) open manifolds with positive Ricci curvature, sectional curvature bounded from below and infinite Betti numbers $b_2,b_n$, moreover its volume growth can be arbitrarily close to quadratic volume growth. Compared with some known result of finite topology for manifolds with nonnegative Ricci curvature and lower sectional curvature bound, it makes sense to ask whether complete manifolds with such curvature bounds must be of finite topological type or not provided with at most quadratic volume growth.

math.DG↗

arXiv2021

Manifolds of positive Ricci curvature, quadratically asymptotically nonnegative curvature, and infnite Betti numbers

In a previous paper, we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimension $\ge 6$. The purpose of the present paper is to use a different way to exhibit a family of complete $I$-dimensinal ($I\ge5$) Riemannian manifolds of positive Ricci curvature, quadratically asymptotically nonnegative sectional curvature, and certain infinite Betti number $b_j$ ($2\le j\le I-2$).

math.DG↗

arXiv2019

Examples of manifolds of positive Ricci curvature with quadratically nonnegatively curved infinity and infinite topological type

In this paper, we construct a complete n-dim Riemannian manifold with positive Ricci curvature, quadratically nonnegatively curved infinity and infinite topological type. This gives a negative answer to a conjecture by Jiping Sha and Zhongmin Shen in the case of n greater than or equal to 6.

math.DG↗