13 citations · 20 across the 15 of their papers we have counts for
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Some applications of heat flow to Laplace eigenfunctions
Bogdan Georgiev, Mayukh Mukherjee
We consider mass concentration properties of Laplace eigenfunctions , that is, smooth functions satisfying the equation , on a smooth closed Riemannian manifold.…
Heat profile, level sets and hot spots of Laplace eigenfunctions
Mayukh Mukherjee, Soumyajit Saha
We use probabilistic tools based on Brownian motion and Feynman-Kac formulae to investigate the heat profile for the ground state Dirichlet and second Neumann eigenfunctions. Among…
Mass non-concentration at the nodal set and a sharp Wasserstein uncertainty principle
Mayukh Mukherjee
We prove -mass concentration properties of Laplace eigenfunctions away from their nodal sets, extending a recent result in \cite{GM3} to all dimensions, and giving a slight re…
Nodal sets of Laplace eigenfunctions under small perturbations
Mayukh Mukherjee, Soumyajit Saha
We study the stability properties of nodal sets of Laplace eigenfunctions on compact manifolds under specific small perturbations. We prove that nodal sets are fairly stable if sai…
Polyhedral billiards, eigenfunction concentration and almost periodic control
Mihajlo Cekić, Bogdan Georgiev, Mayukh Mukherjee
We study dynamical properties of the billiard flow on convex polyhedra away from a neighbourhood of the non-smooth part of the boundary, called ``pockets''. We prove there are only…
On maximizing the fundamental frequency of the complement of an obstacle
Bogdan Georgiev, Mayukh Mukherjee
Let be a bounded domain satisfying a Hayman-type asymmetry condition, and let be an arbitrary bounded domain referred to as "obstacle". We are interes…
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…
Boundedness of spectral multipliers of generalized Laplacians on compact manifolds with boundary
Mayukh Mukherjee
Consider a second order, strongly elliptic negative semidefinite differential operator (maybe a system) on a compact Riemannian manifold with smooth boundary, wh…
Extremal values of the (fractional) Weinstein functional on the hyperbolic space
Mayukh Mukherjee
We make a study of Weinstein functionals, first defined in ~\cite{W}, on the hyperbolic space . We are primarily interested in the existence of Weinstein functional m…
Nonlinear travelling waves on non-Euclidean spaces
Mayukh Mukherjee
We study travelling wave solutions, that is, solutions of the form , to nonlinear Schrödinger and Klein-Gordon equations on Riemannian manifolds, both co…