806 citations · 852 across the 16 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…
On the lower bound of the inner radius of nodal domains
Bogdan Georgiev
We discuss the asymptotic lower bound on the inner radius of nodal domains that arise from Laplacian eigenfunctions on a closed Riemannian manifold . First, in the…
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…