3 papers
math.SP2026
Nodal Domains on Surfaces under Perturbation: Upper Semicontinuity, Courant-Sharpness, and Boundary Intersections
Saikat Maji, Mayukh Mukherjee, Soumyajit Saha
We study how the number of nodal domains of eigenfunctions of Schrödinger operators on closed surfaces changes under smooth perturbations of along conv…
math.GR2026
Spectral Dehn functions and a characterisation of word-hyperbolicity
Mayukh Mukherjee
We introduce a \emph{spectral Dehn function} \[ Î_{\mathcal{P}}(n):=\inf λ_1(Î), \] where is the first Dirichlet eigenvalue of the random-walk Laplacian on a van Kamp…
math.SP2026
An Approximate Inverse Spectral Theorem for Manifolds of Constant Negative Curvature
Mayukh Mukherjee
A classical theorem of Colin de Verdière shows that on a closed manifold of fixed topology one can prescribe an arbitrary finite portion of the Laplace-Beltrami spectrum (includin…