Location of hot spots in thin curved strips
Analysis of PDEs
2019-05-21 v2 Mathematical Physics
math.MP
Probability
Spectral Theory
Abstract
The maxima and minima of Neumann eigenfunctions of thin tubular neighbourhoods of curves on surfaces are located in terms of the maxima and minima of Neumann eigenfunctions of the underlying curves. In particular, the hot spots conjecture for a new large class of domains (possibly non-convex and non-Euclidean) is proved.
Keywords
Cite
@article{arxiv.1709.01279,
title = {Location of hot spots in thin curved strips},
author = {David Krejcirik and Matěj Tušek},
journal= {arXiv preprint arXiv:1709.01279},
year = {2019}
}
Comments
This version contains an improved convergence result, which also simplifies the final steps of the proof of the main theorem