Variational formulas for Robin’s constants on pseudoconvex
domains
(à la Yamaguchi)
Mr. Shu-Fai 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 real-analytic 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 |
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All are welcome |
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