English

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