Overview
Dr. Li is an Assistant Professor in the Department of Mathematics, Statistics and Physics at ÌÒÖÓ°Ôº. He earned his Ph.D. from University of California, San Diego in 2017, under the guidance of Professors Lei Ni and Ben Chow. Prior to his current position, Dr. Li was a Visiting Assistant Professor at the University of California, Irvine from 2017 to 2020, where he worked with Professor Richard Schoen, and he also held a Britton Postdoctoral Fellowship at McMaster University from 2020 to 2021.
Dr. Li specializes in Geometric Analysis, employing partial differential equations to investigate the geometric and topological properties of spaces such as Riemannian manifolds. His research interests include Ricci flow, Ricci solitons, °Ã¤³ó±ô±ð°ù-Ricci flow, curvature and topology, the curvature operator of the second kind, Einstein four-manifolds, Gauss curvature flow, modulus of continuity estimates, eigenvalue problems, heat kernels, Robin boundary conditions, matrix Li-Yau-Hamilton estimates, and parabolic frequencies.
Information
Geometric Analysis
Differential Geometry
Partial Differential Equations
Analysis
Geometry
Algebra
- Li, Xiaolong. New sphere theorems under curvature operator of the second kind,
- Li, Xiaolong; Liu, Hao-Yue; Ren, Xin-An. Matrix Li-Yau-Hamilton estimates under °Ã¤³ó±ô±ð°ù-Ricci flow,
- Li, Xiaolong; Wang, Kui. Robin heat kernel comparison on manifolds,
- Li, Xiaolong; Wang, Kui; Wu, Haotian. The second Robin eigenvalue in non-compact rank-1
symmetric spaces,
- Li, Xiaolong, Wang, Kui; Wu, Haotian. An upper bound for the first nonzero Steklov eigenvalue, ESAIM Control Optim. Calc. Var., 31 (2025), Paper No. 5.
- Li, Xiaolong. Product manifolds and the curvature operator of the second kind, Pacific J. Math, 332 (2024), no. 1, 167-193.
- Li, Xiaolong; Tu, Yucheng; Wang, Kui. On a class of quasilinear operators on smooth metric measure spaces, Comm. Anal. Geom., 32 (2024) no. 10, 2757-2803.
- Fluck, Harry; Li, Xiaolong. The curvature operator of the second kind in dimension three, J. Geom. Anal. 34 (2024), no.6, Paper No. 187, 19pp.
- Li, Xiaolong; Zhang, Yongjia. °Ã¤³ó±ô±ð°ùity of Einstein four-manifolds, Math. Z. 307 (2024), no. 1, Paper No. 4, 10pp.
- Li, Xiaolong. Manifolds with nonnegative curvature operator of the second kind, Commun. Contemp. Math. 26 (2024), no.3 Paper No. 2350003, 26pp.
- Li, Xiaolong; Zhang, Qi S. Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency, Calc. Var. Partial Differential Equations. 63 (2024), no.3, Paper No. 63, 38pp.
- Li, Xiaolong, Wang, Kui; Wu, Haotian. On the second Robin eigenvalue of the Laplacian, Calc. Var. Partial Differential Equations. 62 (2023), no. 9, Paper No. 256, 17 pp.
- Li, Xiaolong. °Ã¤³ó±ô±ð°ù manifolds and the curvature operator of the second kind. Math. Z. 303 (2023), no. 4, Paper No. 101, 26 pp.
- Li, Xiaolong. °Ã¤³ó±ô±ð°ù surfaces with six-positive curvature operator of the second kind, Proc. Amer. Math. Soc. 151 (2023), no. 11, 4909-4922.
- Li, Xiaolong; Wang, Kui. Eigenvalue estimates on quaternion-°Ã¤³ó±ô±ð°ù manifolds. J. Geom. Anal. 33 (2023), no. 3, Paper No. 85, 20 pp.
- Li, Xiaolong; Zhang, Yongjia. Ancient solutions to the Ricci flow in higher dimensions, Comm. Anal. Geom. 30 (2022), no. 9, 2011-2048.
- Li, Xiaolong, Manifolds with 4.5-positive curvature operator of the second kind. J. Geom. Anal. 32 (2022), no. 11, Paper No. 281, 14 pp.
- Li, Xiaolong; Wang, Kui. Sharp lower bound for the first eigenvalue of the weighted p-Laplacian II. Math. Res. Lett. 28 (2021), no. 5, 1459–1479.
- Li, Xiaolong; Wang, Kui. Lower bounds for the first eigenvalue of the Laplacian on °Ã¤³ó±ô±ð°ù manifolds. Trans. Amer. Math. Soc. 374 (2021), no. 11, 8081-8099.
- Li, Xiaolong; Wang, Kui. Sharp lower bound for the first eigenvalue of the weighted p-Laplacian I. J. Geom. Anal. 31 (2021), no. 8, 8686-8708.
- Li, Xiaolong. Modulus of continuity estimates for fully nonlinear parabolic equations. Calc. Var. Partial Differential Equations 60 (2021), no. 5, Paper No. 182, 23 pp.
- Li, Xiaolong; Wang, Kui. First Robin eigenvalue of the p-Laplacian on Riemannian manifolds. Math. Z. 298 (2021), no. 3-4, 1033–1047.
- Li, Xiaolong; Ni, Lei. °Ã¤³ó±ô±ð°ù-Ricci shrinkers and ancient solutions with nonnegative orthogonal bisectional