Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: La g\'eom\'etrie de Bakry-\'Emery et l'\'ecart fondamental   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.

8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg