5 papers · 1 filter
Unbounded Topology of Nodal Sets of Harmonic Functions
Robert Koirala
For every integer \(n\ge 3\), every \(1\le \ell\le n-2\), and every sufficiently large integer \(m\), we construct harmonic functions \(u_{m,\ell}\) on the unit ball \(B_1(0)\subse…
Nested nodal loops for sums of Laplace eigenfunctions
Robert Koirala
We study nested loops in zero sets of sums of Laplace eigenfunctions on closed surfaces. In the real-analytic category, answering a question of Logunov, we prove a uniform bound fo…
Nested nodal loops of biharmonic functions
Javier Gómez-Serrano, Robert Koirala, Alexander Logunov
Given any \(n\in\mathbb{N}\), we construct a real-valued biharmonic polynomial on \(\mathbb{R}^2\) whose zero set contains a nest of \(n\) smooth, disjoint topological loops, meani…
Equidistribution of Eigenfunctions of Quantum Cat Maps
Robert Koirala
We prove that the short-period eigenfunctions of quantum cat maps constructed by Kim and the author equidistribute on in the sense of semiclassical measures. We also…
Structure Theory of Parabolic Nodal and Singular Sets
Max Hallgren, Robert Koirala, Zilu Ma
We establish new estimates for the size and structure of the nodal set and the singular set of solutions to parabolic inequalities with parabolic…