12 citations · 54 across the 27 of their papers we have counts for
8 papers · 1 filter
Product manifolds and the curvature operator of the second kind
Xiaolong Li
We investigate the curvature operator of the second kind on product Riemannian manifolds and obtain some optimal rigidity results. For instance, we prove that the universal cover o…
Robin heat kernel comparison on manifolds
Xiaolong Li, Kui Wang
We investigate the heat kernel with Robin boundary condition and prove comparison theorems for heat kernel on geodesic balls and on minimal submanifolds. We also prove an eigenvalu…
The second Robin eigenvalue in non-compact rank-1 symmetric spaces
Xiaolong Li, Kui Wang, Haotian Wu
In this paper, we prove a quantitative spectral inequality for the second Robin eigenvalue in non-compact rank-1 symmetric spaces. In particular, this shows that for bounded domain…
Kähler manifolds and the curvature operator of the second kind
Xiaolong Li
This article aims to investigate the curvature operator of the second kind on Kähler manifolds. The first result states that an -dimensional Kähler manifold with $\frac{3}{2}(m^…
Kähler surfaces with six-positive curvature operator of the second kind
Xiaolong Li
The purpose of this article is to initiate the investigation of the curvature operator of the second kind on Kähler manifolds. The main result asserts that a closed Kähler surface…
Kählerity of Einstein four-manifolds
Xiaolong Li, Yongjia Zhang
We prove that a closed oriented Einstein four-manifold is either anti-self-dual or (after passing to a double Riemann cover if necessary) Kähler-Einstein, provided that $λ_2 \geq -…