2 papers
math.CO2026
Urschel Nodal Domains via Perturbation Theory
Joel Friedman, Tong Ling, Soumyajit Saha
We prove several types of Courant nodal domain theorems for generalized Laplacians on graphs, based on an invariant introduced by Urschel, which we call the "Urschel number", denot…
math.SP2025
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 conver…