University Research Professor PhD Peking Alexander von Humboldt Research Fellow, 1999 Dean of Science Distinguished Scholar Medal, 2009
Office: HH3044 Phone: (709) 8648072 Fax: (709) 8643010
Personal website


Dr. Xiao's research and teaching interests lie in geometric analysis and partial differential equations. In particular, Dr. Xiao works on the interactions between harmonic analysis, complex variables and operator theory, but also applies techniques coming from function spaces and potential theory to the study of conformaldifferential geometry and heat equations, NavierStokes equations and wave equations. Here are some of his recent articles:
 Isoperimetry for semilinear torsion problems in Riemannian twomanifolds, Adv. Math. 229(2012)23792404.
 (with D. R. Adams) Morrey potentials and harmonic maps, Comm. Math. Phys. 308(2011)439456.
 L^pGreen potential estimates on noncompact Riemannian manifolds, J. Math. Physics, 51, 063515(2010)117.
 Toward best isoperimetric constants for (H^{1},BMO)normal conformal metrics on R^{n}, n>=3, Adv. Math. 220(2009)540559.
 The Qp Carleson measure problem, Adv. Math. 217(2008)20752088.
 Sharp Sobolev and isoperimetric inequalities split twice, Adv. Math. 211(2007)417435.
 Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation, Adv. Math. 207(2006)828846.
Meanwhile, Dr. Xiao is the author of the following textbooks and monographs:
 Integral and Functional Analysis, Nova Science Publishers, 2008.
 Geometric Qp Functions, Frontiers in Math., BirkhauserVerlag, 2006.
 Elementary Number Theory, International Press, 2006.
 Holomorphic Q Classes, Lecture Notes in Math. 1767, SpringerVerlag, 2001.
In addition, Dr. Xiao serves as an Associate Editor of:
 Canadian Journal of Mathematics.
 Canadian Mathematical Bulletin.
 Journal of Mathematical Analysis and Applications.
