6 citations · 13 across the 10 of their papers we have counts for
14 papers
Inradius of random lemniscates
Manjunath Krishnapur, Erik Lundberg, Koushik Ramachandran
A classically studied geometric property associated to a complex polynomial is the inradius (the radius of the largest inscribed disk) of its (filled) lemniscate $Λ:= \{z \in \…
Conformal Rigidity of Polar Set Complements
Ratna Pal, Koushik Ramachandran, Sivaguru Ravisankar
Let be a closed polar subset of . In this short note, we use elementary potential theoretic tools to show that any conformal map on is nece…
A note on the critical points of the localization landscape
Erik Lundberg, Koushik Ramachandran
Let be a bounded domain. In this note, we use complex variable methods to study the number of critical points of the function that solves the elliptic…
The closed range property for the -operator on planar domains
A. -K. Gallagher, J. Lebl, K. Ramachandran
Let be an open set. We show that has closed range in if and only if the Poincaré-Dirichlet inequality holds. Moreover, we give…
Random Bernstein-Markov factors
Igor Pritsker, Koushik Ramachandran
For a polynomial of degree , Bernstein's inequality states that for all norms on the unit circle, with equality for $P_n(z)=…
Natural boundary and zero distribution of random polynomials in smooth domains
Igor Pritsker, Koushik Ramachandran
We consider the zero distribution of random polynomials of the form , where are non-trivial i.i.d. complex random variabl…
The arc length of a random lemniscate
Erik Lundberg, Koushik Ramachandran
A polynomial lemniscate is a curve in the complex plane defined by . Erdös, Herzog, and Piranian posed the extremal problem of determining the maximu…
Equidistribution of zeros of random polynomials
Igor Pritsker, Koushik Ramachandran
We study the asymptotic distribution of zeros for the random polynomials , where are non-trivial i.i.d. complex random va…
Harnack inequality for non-local Schrödinger operators
Siva Athreya, Koushik Ramachandran
Let , and be a twice differentiable function with all second partial derivatives being continuous. For $1\l…
Electrostatic skeletons
Alexandre Eremenko, Erik Lundberg, Koushik Ramachandran
Let u be the equilibrium potential of a compact set K. An electrostatic skeleton of K is a positive measure whose closed support has connected complement and no interior, and whose…
Asymptotic behavior of positive harmonic functions in certain unbounded domains
Koushik Ramachandran
We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling,…
A Pinching constant for harmonic manifolds
K. Ramachandran, Akhil Ranjan
In this note we shall show that the sectional curvature of a harmonic manifold is bounded on both sides. In fact we shall give a pinching constant for all harmonic manifolds. We sh…
Harmonic manifolds with some specific volume densities
K. Ramachandran, Akhil Ranjan
We show that noncompact simply connected harmonic manifolds with volume density is isometric to the real hyperbolic space and noncompact simply connected…
Finite dimensional imbeddings of harmonic spaces
K. Ramachandran, Akhil Ranjan
In a noncompact harmonic manifold we establish finite dimensionality of the eigenspaces generated by radial eigenfunctions of the form . As a consequence, fo…