arXiv subjects

Xiaodong Yan

Publications and source records attributed to Xiaodong Yan.

38 records · Page 3Linked to original sources

arXiv2007

An integral equation in conformal geometry

We study the existence of a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class of metrics on a compact manifold with boundary. The question may be reduced to an extremal problem for the harmonic extension of functions and the related nonlinear integral equation is discussed.

math.AP↗

arXiv2006

Sharp integral inequalities for harmonic functions

Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated integral system and some Liouville type theorems.

math.AP↗