Boundary behavior of the Carathéodory and Kobayashi-Eisenman volume elements and the Kobayashi--Fuks metric
Debaprasanna Kar, IISER, Pune
| Speaker |
Debaprasanna Kar, IISER, Pune
|
|---|---|
| When |
Feb 28, 2022
from 04:00 PM to 05:00 PM |
| Where | zoom seminar |
| Contact Name | Pramila |
| Contact Phone | 08066953702 |
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Abstract:
We will compute the boundary asymptotics of the Carathéodory and Kobayashi-Eisenman volume elements on convex finite type domains and Levi corank one domains in C^n using the standard scaling techniques. We will show that their ratio, the so-called C/K ratio or the quotient invariant, can be used to detect strong pseudoconvexity. Some properties of a Kähler metric called the Kobayashi--Fuks metric will also be observed on strongly pseudoconvex domains in C^n. We study the localization of this metric near holomorphic peak points and show that this metric shares several properties with the classical Bergman metric on strongly pseudoconvex domains.