## Overview

Dr. Li is currently an Assistant Professor in the Department of Mathematics, Statistics and Physics at Wichita State University. He obtained his Ph.D. degree from University of California, San Diego in 2017 under the supervision of Prof. Lei Ni and Prof. Ben Chow. Before joining Wichita State, he was a Visiting Assistant Professor at University of California, Irvine supervised by Prof. Richard Schoen from 2017 to 2022, and a Britton Postdoctoral Fellow at McMaster University from 2020 to 2021.

Dr. Li works in Geometric Analysis. He uses tools from partial differential equations to study geometric and topological properties of spaces, such as Riemannian manifolds. Some key words about his research are: Ricci flow and Ricci solitons, Kähler-Ricci flow and Kähler manifolds, curvature and topology, curvature operator of the second kind, Einstein four-manifolds, Gauss curvature flow, two-point maximum principle, modulus of continuity, eigenvalue problems, heat kernel, Robin boundary condition, matrix Li-Yau-Hamilton estimates, and parabolic frequency.

## Information

Geometric Analysis

Differential Geometry

Partial Differential Equations

Analysis

Geometry

Algebra

- Li, Xiaolong; Liu, Hao-Yue; Ren, Xin-An. Matrix Li-Yau-Hamilton estimates under Kähler-Ricci flow, arXiv2307.10920
- Li, Xiaolong. Product manifolds and the curvature operator of the second kind, arXiv:2209.02119
- Li, Xiaolong; Wang, Kui. Robin heat kernel comparison on manifolds, arXiv:2208.13402
- Li, Xiaolong; Wang, Kui; Wu, Haotian. The second Robin eigenvalue in non-compact rank-1
symmetric spaces, arXiv:2208.07546
- Li, Xiaolong, Wang, Kui; Wu, Haotian. An upper bound for the first nonzero Steklov eigenvalue, arXiv:2003.03093
- Li, Xiaolong; Zhang, Yongjia. Kählerity of Einstein four-manifolds, Math. Z., to appear, arXiv:2206.04870
- Fluck, Harry; Li, Xiaolong. The curvature operator of the second kind in dimension three, J. Geom. Anal., to appear, arXiv:2303.17663
- Li, Xiaolong; Tu, Yucheng; Wang, Kui. On a class of quasilinear operators on smooth metric measure spaces, Comm. Anal. Geom., to appear.
- 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.
- Li, Xiaolong. Manifolds with nonnegative curvature operator of the second kind, Commun. Contemp. Math., 26 (2024), no.3 Paper No. 2350003.
- Li, Xiaolong, Wang, Kui; Wu, Haotian. On the second Robin eigenvalue of the Laplacian, Calc. Var. Partial Differential Equations., 62, 256 (2023).
- Li, Xiaolong. Kähler surfaces with six-positive curvature operator of the second kind, Proc. Amer. Math. Soc., 151 (2023), 4909-4922.
- Li, Xiaolong. Kähler manifolds and the curvature operator of the second kind. Math. Z. 303 (2023), no. 4, Paper No. 101, 26 pp.
- Li, Xiaolong; Wang, Kui. Eigenvalue estimates on quaternion-Kähler 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 Kähler 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. Kähler-Ricci shrinkers and ancient solutions with nonnegative orthogonal bisectional curvature. J. Math. Pures Appl. (9) 138 (2020), 28–45.
- Li, Xiaolong; Wang, Kui. Parabolic frequency monotonicity on compact manifolds. Calc. Var. Partial Differential Equations 58 (2019), no. 6, Paper No. 189, 18 pp.
- Li, Xiaolong; Ni, Lei; Wang, Kui. Four-dimensional gradient shrinking solitons with positive isotropic curvature. Int. Math. Res. Not. IMRN 2018, no. 3, 949–959.
- Li, Xiaolong; Wang, Kui. Nonparametric hypersurfaces moving by powers of Gauss curvature. Michigan Math. J. 66 (2017), no. 4, 675–682.
- Li, Xiaolong; Wang, Kui. Moduli of continuity for viscosity solutions on manifolds. J. Geom. Anal. 27 (2017), no. 1, 557–576.
- Li, Xiaolong. Moduli of continuity for viscosity solutions. Proc. Amer. Math. Soc. 144 (2016), no. 4, 1717–1724.

2023-2025: LEAPS-MPS, National Science Foudation, $250,000

2022-2027: Travel Support for Mathematicians, Simons Foundation, $42,000.

- 2021 - present: Co-organizer of WSU Math Circle since 2021.
- 2022 - present: AMC 8 Competition Manager.
- 2022 - present: Co-organizer of the Geometry, Topology, and Analysis Seminar at WSU
- October 2024: Co-organzier of AMS Fall Western Sectional Meeting at UC Riverside.
- April 2024: Co-organizer of the Kansas Geometric Analysis Conference at WSU.
- March 2023: Co-organizer of the Midwest Geometry Conference at Kansas State University.
- March 2022: Co-organizer of the Midwest Geometry Conference at WSU.
- 2021: Co-organizer of the Geometry and Topology Seminar at WSU
- 2021: Co-organizer of International Conference on Recent Developments in Geometric Analysis