4 papers · 2 filters
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…