### Quantitative isoperimetric inequalities for the Robin Laplacian

Analysis and Geometry Seminar

25th April 2019, 3:15 pm – 4:15 pm

Howard House, 4th Floor Seminar Room

In this talk I will prove a quantitative form of the Faber-Krahn inequality for the first Robin-Laplacian eigenvalue. The key of the proof is based on the analysis of solutions of an auxiliary free discontinuity problem which, for a given set, produces a new one with almost the same Fraenkel asymmetry and lower eigenvalue. Further implications of this technique to other isoperimetric inequalities, like Saint Venant, will be discussed.

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