The "Hot Spots" Conjecture on the Vicsek Set
Functional Analysis
2019-01-04 v2
Abstract
We prove the Hot Spot conjecture on the Vicsek set. Specifically, we show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set attains its maximum and minimum on the boundary.
Cite
@article{arxiv.1806.05275,
title = {The "Hot Spots" Conjecture on the Vicsek Set},
author = {Marius Ionescu and Thomas L. Savage},
journal= {arXiv preprint arXiv:1806.05275},
year = {2019}
}
Comments
We made changes suggested by the anonymous referee and editors. The paper is accepted for publication in the Special Issue on Harmonic Analysis: Smooth and Non-Smooth, Demonstratio Mathematica