arXiv subjects

Huiya He

Publications and source records attributed to Huiya He.

3 recordsLinked to original sources

arXiv2021

Critical metrics of the volume functional on three-dimensional manifolds

In this paper, we prove the three-dimensional $CPE$ conjecture with non-negative Ricci curvature. Moreover, we establish a classification result on three-dimensional vacuum static space with non-negative Ricci curvature. Finally, we show that a three-dimensional compact, oriented, connected Miao-Tam critical metric with smooth boundary, non-negative Ricci curvature and non-negative potential function is isometric to a geodesic ball in a simply connected space form $\mathbb{R}^3$ or $\mathbb{S}^3$.

math.DG↗

arXiv2018

On compact Riemannian manifolds with harmonic weyl curvature

We give some rigidity theorems for an n$(\geq4)$-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $σ_2$. Moreover, when $n=4,$ we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positive constant $σ_2$ is isometric to a quotient of the round $\mathbb{S}^4$.

math.DG↗

arXiv2018

Rigidity theorem for compact Bach-flat manifolds with positive constant $σ_2$

We prove that an n($\geq$ 4)-dimensional compact Bach-flat manifold with positive constant $σ_2$ is an Einstein manifold, provided that its Weyl curvature satisfies a suitable pinching condition.

math.DG↗