讲座标题：Quasi-extremal distance (QED) constants and boundary quasiconformal reflection constants
主讲人： 程涛 副教授
This talk is devoted to the study of some fundamental problems on modulus and extremal length of curve families, capacity, and n-harmonic functions in the Euclidean space R^n. One of the main goals is to establish the existence, uniqueness, and boundary behavior of the extremal function for the conformal capacity of a capacitor in R^n. This generalizes some well known results and has its own interests in geometric function theory and potential theory. It is also used as a major ingredient in this paper to establish a sharp upper bound for the quasi-extremal distance constant of a domain in terms of its local boundary quasiconformal reflection constant. Along the way, several interesting results are established for modulus and extremal length. One of them is a decomposition theorem for the extremal length of the curve family joining two disjoint continua in a domain.