Geometry Seminar

Variational formulas for Robin’s constants on pseudoconvex domains

(à la Yamaguchi)


Mr. Shu-Fai Chan

Department of Mathematics, The University of Hong Kong



Let D be an unramified covering domain over an open set in equ, equ, with smooth boundary. For each fixed point equ in D, let eqube Green's function on D with the pole at equ with respect to the Euclidean metric. The Robin constant at the point equ is defined as


When D is a smoothly bounded pseudoconvex domain over equ, Hiroshi Yamaguchi proved that both equ and equ are real-analytic strictly plurisubharmonic exhaustion functions on  D.

Yamaguchi's method is to study variations of domainsequ. By using a variational formula for equ 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 equ 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.



November 3, 2005 (Thursday)


4:00 – 5:00pm


Room 517, Meng Wah Complex




All are welcome