13 citations · 20 across the 15 of their papers we have counts for
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A Spectral Gap Estimate and Applications
Bogdan Georgiev, Mayukh Mukherjee, Stefan Steinerberger
We consider the Schrödinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where is bounded from below and p…
Some remarks on nodal geometry in the smooth setting
Bogdan Georgiev, Mayukh Mukherjee
We consider a Laplace eigenfunction on a smooth closed Riemannian manifold, that is, satisfying . We introduce several observations about the geometry of its van…
Nodal Geometry, Heat Diffusion and Brownian Motion
Bogdan Georgiev, Mayukh Mukherjee
We use tools from -dimensional Brownian motion in conjunction with the Feynman-Kac formulation of heat diffusion to study nodal geometry on a compact Riemannian manifold . On…
Variation of Laplace spectra of compact "nearly" hyperbolic surfaces
Mayukh Mukherjee
We use the time real analyticity of Ricci flow proved by Kotschwar to extend a result in ~\cite{B}, namely, we prove that the Laplace spectra of negatively curved compact surfaces…