Variational formulas for Robin’s constants on pseudoconvex
domains
(à la Yamaguchi)
Mr. ShuFai Chan
Abstract
Let D be an unramified covering domain over an open set in _{}, _{}, with smooth boundary. For each fixed point _{} in D, let _{}be Green's function on D with the pole at _{} with respect to the Euclidean metric. The Robin constant at the point _{} is defined as
_{}
When D is a smoothly bounded pseudoconvex domain over _{}, Hiroshi Yamaguchi proved that both _{} and _{} are realanalytic strictly plurisubharmonic exhaustion functions on D.
Yamaguchi's method is to study variations of domains_{}. By using a variational formula for _{} in terms of the boundary behavior of Green's function, he was able to apply boundary condition of certain type of pseudoconvex domain with smooth boundary and proved that _{} is superharmonic. This result was then applied to get the main theorem, where the total space is only assumed to be pseudoconvex. In this talk, we shall examine his method in detail.
Date: 
November 3, 2005 (Thursday) 
Time: 
4:00 – 5:00pm 
Place: 
Room 517, Meng Wah Complex 

All are welcome 
