讲座内容简介：

        This talk will address two optimal inequalities inserting electric capacity between entropy flux and graphical mass.

讲座人简介：

Jie Xiao，University Research Professor; PhD Peking, 1992; Alexander von Humboldt Research Fellow, 1999; Dean of Science Distinguished Scholar Medal, 2009.

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 conformal-convex-differential geometry and heat-type equations and Navier-Stokes equations. Here are some of his recent articles:

• P-capacity vs surface-area, Adv. Math. 208(2017)1318-1336

• Isoperimetry for semilinear torsion problems in Riemannian two-manifolds, Adv. Math. 229(2012)2379-2404

• Toward best isoperimetric constants for (H1,BMO)-normal conformal metrics on Rn, n>=3, Adv. Math. 220(2009)540-559

• The Qp Carleson measure problem, Adv. Math. 217(2008)2075-2088

• Sharp Sobolev and isoperimetric inequalities split twice, Adv. Math. 211(2007)417-435

• Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation, Adv. Math. 207(2006)828-846

Meanwhile, Dr. Xiao is the author of the following monographs and textbooks:

• Qa Analysis on Euclidean Spaces, De Gruyter, 2019

• Integral and Functional Analysis, Nova Science Publishers, 2008

• Geometric Qp Functions, Frontiers in Math., Birkhauser-Verlag, 2006

• Elementary Number Theory, International Press, 2006

• Holomorphic Q Classes, Lecture Notes in Math. 1767, Springer-Verlag, 2001

In addition, Dr. Xiao serves as:

• Founding Editor-in-Chief of the Advances in Analysis and Geometry

• Editor-in-Chief of the Canadian Mathematical Bulletin

• Associate Editor of the Journal of Mathematical Analysis and Applications