Xiaolong Li, Assistant Professor

Mathematics, PhD, University of California, San Diego, 2017

 

Contact

Research

Xiaolong Li works in Geometric Analysis, which includes both the use of geometrical methods in the study of partial differential equations and the application of the theory of partial differential equations to differential geometry. His current research focuses on the following aspects of geometric analysis: 

(1). Ricci flow and other geometric flows;
(2). Nonlinear elliptic and parabolic partial differential equations.
(3). Modulus of continuity estimates and their applications;
(4). Eigenvalue problems in geometry.

Selected Publications

  • 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–ß576.
  • Li, Xiaolong. Moduli of continuity for viscosity solutions. Proc. Amer. Math. Soc. 144 (2016), no. 4, 1717–1724.