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-differential geometry and heat equations, Navier-Stokes equations and wave equations. Here are some of his recent articles:
· Geometrical logarithmic capacitance, Adv. Math. 365(2020)107048.
· 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 textbooks and monographs:
· Qα 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.

Jie Xiao, PhD University Research Professor, Memorial University of Newfoundland, Canada

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-differential geometry and heat equations, Navier-Stokes equations and wave equations. Here are some of his recent articles:
· Geometrical logarithmic capacitance, Adv. Math. 365(2020)107048.
· 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 textbooks and monographs:
· Qα 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.

Showing the single result

Showing the single result