La g\'eom\'etrie de Bakry-\'Emery et l'\'ecart fondamental

Julie Rowlett

doi:10.5802/tsg.282

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arXiv · 2012.06518

La g\'eom\'etrie de Bakry-\'Emery et l'\'ecart fondamental

Julie Rowlett

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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.

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BibTeX RIS

Julie Rowlett. 2020-12-11. La g\'eom\'etrie de Bakry-\'Emery et l'\'ecart fondamental. https://doi.org/10.5802/tsg.282

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