5 citations · 17 across the 13 of their papers we have counts for
14 papers
Holomorphic mappings of finitely connected planar domains
Jaikrishnan Janardhanan
Results on holomorphic mappings of finitely connected planar domains are often proved using Koebe's famous circle mapping theorem. A prominent example is Julia's bound on the size…
Uniformization of domains in the Riemann sphere via the Kobayashi metric
Jaikrishnan Janardhanan
We prove the uniformization theorem for domains in the Riemann sphere via the Kobayashi metric. Our proof does not rely on the existence of the elliptic modular function and instea…
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…
Proper holomorphic mappings onto symmetric products of a Riemann surface
Gautam Bharali, Indranil Biswas, Divakaran Divakaran +1
We show that the structure of proper holomorphic maps between the -fold symmetric products, , of a pair of non-compact Riemann surfaces and , provided these are…
Finiteness theorems for holomorphic mappings from products of hyperbolic Riemann surfaces
Divakaran Divakaran, Jaikrishnan Janardhanan
We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal…
Finiteness Theorems for Products and Symmetric Products of Hyperbolic Riemann Surfaces
Divakaran Divakaran, Jaikrishnan Janardhanan
We prove that if is a product of hyperbolic Riemann surfaces of finite type and is a complex manifold, where is a bounded simply-con…
Proper holomorphic mappings of balanced domains in
Jaikrishnan Janardhanan
We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in . Specifically: we prove that any proper holomorphic se…
Proper holomorphic maps between bounded symmetric domains revisited
Gautam Bharali, Jaikrishnan Janardhanan
We prove that a proper holomorphic map between two bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give…
Proper holomorphic mappings between hyperbolic product manifolds
Jaikrishnan Janardhanan
We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case…