12 citations · 54 across the 27 of their papers we have counts for
29 papers
Non-existence of Lyapunov exponents in the Newhouse domain
Shin Kiriki, Xiaolong Li, Yushi Nakano +1
We show that within the Newhouse domain of surface diffeomorphisms (), there exists a dense subset such that for any , Lyapu…
Matrix Li-Yau-Hamilton Estimates under Kähler-Ricci Flow
Xiaolong Li, Hao-Yue Liu, Xin-An Ren
We prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Kähler-Ricci flow. As an appli…
Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency
Xiaolong Li, Qi S. Zhang
In this paper we prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We t…
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…