7 papers · 1 filter
Revisiting Kobayashi hyperbolicity on planar domains
Bharathi Thiruvengadam, Jaikrishnan Janardhanan
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 co…
Finiteness of the fixed point sets of automorphisms
Bharathi Thiruvengadam, Jaikrishnan Janardhanan
We investigate the size of fixed point sets of automorphisms of bounded domains in . In one complex variable, a nontrivial automorphism has at most two fixed points,…
Conformal Mappings Through the Lens of Invariant Metrics
Bharathi Thiruvengadam, Jaikrishnan Janardhanan
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 pro…
Schwarz lemmas via the pluricomplex Green's function
Jaikrishnan Janardhanan
We prove a version of the Schwarz lemma for holomorphic mappings from the unit disk into the symmetric product of a Riemann surface. Our proof is function-theoretic and self-contai…
A -point Quadrature domain of order not biholomorphic to a balanced domain
Pranav Haridas, Jaikrishnan Janardhanan
It is known that if is a polynomial biholomorphism with polynomial inverse and constant Jacobian then is a -point Quadrature domain (the Bergman span cont…
A note on the smoothness of the Minkowski function
Pranav Haridas, Jaikrishnan Janardhanan
The Minkowski function is a crucial tool used in the study of balanced domains and, more generally, quasi-balanced domains in several complex variables. If a quasi-balanced domain…