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 $-{\Delta }_{g_t}+V_t$ on closed surfaces changes under smooth perturbations of $(g_t,V_t)$ along conver…