arXiv subjects

Bharathi Thiruvengadam

Publications and source records attributed to Bharathi Thiruvengadam.

3 recordsLinked to original sources

arXiv2026

Revisiting Kobayashi hyperbolicity on planar domains

We give two new elementary proofs of the complete Kobayashi hyperbolicity of the twice-punctured complex plane. We also present an extremely short proof that bounded domains are complete Kobayashi hyperbolic. Our proofs rely neither on the fact that the universal cover of the twice-punctured plane is the disk nor on the existence of negatively curved metrics. As applications, we present concise proofs of the classical theorems of Landau, Schottky, and Picard. Finally, we provide a characterization of Kobayashi hyperbolicity for planar domains inspired by a similar result of Hahn.

math.CV↗

arXiv2026

Finiteness of the fixed point sets of automorphisms

We investigate the size of fixed point sets of automorphisms of bounded domains in $\mathbb{C}^n$. In one complex variable, a nontrivial automorphism has at most two fixed points, but in higher dimensions fixed point sets need not be discrete. We show, under natural extension hypotheses, that discreteness forces finiteness. We also obtain a uniform bound for the number of fixed points of automorphisms in compact subgroups whose elements admit such extensions.

math.CV↗

arXiv2025

Conformal Mappings Through the Lens of Invariant Metrics

The main objective of this paper is to show that balls under invariant metrics on hyperbolic planar domains are finitely-connected. As applications, we give new and transparent proofs of classical results on conformal mappings of planar domains. In particular, we show that any conformal self-map of a hyperbolic planar domain with three fixed points is the identity. We also give a new and very simple proof of the theorem by Aumann and Carathéodory that states that the isotropy groups of a hyperbolic planar domain are either finite or the domain is simply-connected.

math.CV↗