Xiangjin Xu

I. Harmonic Analysis on Manifolds:
the spectral theory of elliptic operators (Laplace operator and Schrödinger operator) on compact or complete manifolds, in particular, on the growth estimates (L^p, bilinear, and gradient estimates) of eigenfunctions, multiplier problems, Carleson measures and Logvinenko-Sereda sets on compact or complete manifolds with or without boundary.

II. Geometric PDEs:
Li-Yau and Hamilton type gradient estimates, sharp estimates for the heat kernel and the Green's function for heat equations and Schrödinger operators on Riemannian manifolds (Finsler manifolds, metric measure spaces). Gradient estimates, Liouville's Theorems and entropy formulae for linear and nonlinear (possible degenerate) parabolic equations. Control theoretic problems for (linear and nonlinear) parabolic and hyperbolic PDE systems on manifolds via Carleman estimates. Periodic solutions, subharmonics and homoclinic orbits of Hamiltonian systems.

At Binghamton since	2007
Office	WH 204
Fax	(607) 777-2450
Email	xxu@binghamton.edu • xxu@math.binghamton.edu

Course	Section	Title	Schedule	Room
Math 371	01	Ordinary Differential Equations	MWF 11:00–12:00	CW-110
Math 478	02	Real Analysis I	MWF 12:15–1:15	FA-354

Areas of Interest