Mayukh Mukherjee

activity

20172021

most citedHeating up decision boundaries: isocapacitory saturation, adversarial scenarios and generalization bounds

1 citations · 1 across the 2 of their papers we have counts for

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math.AP2021

Some applications of heat flow to Laplace eigenfunctions

Bogdan Georgiev, Mayukh Mukherjee

We consider mass concentration properties of Laplace eigenfunctions $φ_{λ}$ , that is, smooth functions satisfying the equation $- Δ φ_{λ} = λ φ_{λ}$ , on a smooth closed Riemannian manifold.…

math.AP2021

Mass non-concentration at the nodal set and a sharp Wasserstein uncertainty principle

Mayukh Mukherjee

We prove $L^{p}$ -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…

math.AP2020

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…

math.AP2019

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…

math.AP2017

On maximizing the fundamental frequency of the complement of an obstacle

Bogdan Georgiev, Mayukh Mukherjee

Let $Ω \subset R^{n}$ be a bounded domain satisfying a Hayman-type asymmetry condition, and let $D$ be an arbitrary bounded domain referred to as "obstacle". We are interes…