La g\'eom\'etrie de Bakry-\'Emery et l'\'ecart fondamental
Spectral Theory
2020-12-14 v1 Analysis of PDEs
Differential Geometry
Abstract
This article is a brief presentation of results surrounding the fundamental gap. We begin by recalling Bakry-Emery geometry and demonstrate connections between eigenvalues of the Laplacian with the Dirichlet and Neumann boundary conditions. We then show a connection between the fundamental gap and Bakry-Emery geometry, concluding with a presentation of the key ideas in Andrews's and Clutterbuck's proof of the fundamental gap conjecture. We conclude with a presentation of results for the fundamental gap of triangles and simplices.
Keywords
Cite
@article{arxiv.2012.06518,
title = {La g\'eom\'etrie de Bakry-\'Emery et l'\'ecart fondamental},
author = {Julie Rowlett},
journal= {arXiv preprint arXiv:2012.06518},
year = {2020}
}
Comments
in French. This is a preliminary version of the published article of the same title, freely available online!