Ph.D Synopsis by Mr.Ravi Shankar Jaiswal
Speaker |
Mr.Ravi Shankar Jaiswal (TIFR CAM)
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When |
Jun 19, 2024
from 10:30 AM to 11:30 AM |
Where | Lecture Hall, First Floor |
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Title
BOUNDARY BEHAVIOUR OF BIHOLOMORPHIC INVARIANTS ON INFINITE TYPE DOMAINS
Abstract
We will prove optimal lower and upper bounds of the Bergman and Szegő kernels near the boundary of bounded smooth generalized decoupled pseudoconvex domains in ℂn+1. Generalized decoupled domains may have complex tangential directions that are not necessarily decoupled individually, and their boundary points may possess both finite and infinite type directions.
We will then proceed to study exponentially flat infinite type domains. On this class of domains, we will prove nontangential asymptotic limits of the following at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in ℂn+1: Bergman kernel and metric, Kobayashi and Kobayashi–Fuks metrics, holomorphic sectional, Ricci and scalar curvatures of the Bergman metric, and Bergman canonical invariant.