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SUMMARY:On the effective sharp stability of the Faber-Krahn inequality
DTSTART:20260924T091500Z
DTEND:20260924T101500Z
DTSTAMP:20261007T164300Z
UID:indico-event-16912@indico.math.cnrs.fr
DESCRIPTION:Speakers: João Miguel Machado\n\nThe Faber–Krahn inequality
  states that\, among sets of fixed volume\, balls minimize the first Diric
 hlet eigenvalue. Its sharp quantitative form controls the square of the Fr
 aenkel asymmetry by the spectral deficit. Brasco\, De Philippis and Velich
 kov proved this estimate through an argument using compactness\, a contrad
 iction step\, and the selection principle of Cicalese-Leonardi\; consequen
 tly\, their stability constant is not computable. In this talk\, we will d
 iscuss a proof with a computable dimensional constant\, resolving Open Pro
 blem 2 in the survey of Brasco and De Philippis. The argument passes throu
 gh the Saint–Venant inequality\, which states that the torsion functiona
 l is maximised by balls. Its two main ingredients are a new level-set char
 acterisation of the torsional deficit and a differential estimate for the 
 distance of the level sets from a moving ball. These ingredients are conne
 cted by the strong quantitative isoperimetric inequality of Fusco and Juli
 n. The Kohler–Jobin inequality then transfers the effective sharp stabil
 ity of the Saint-Venant inequality back to Faber–Krahn.\n \nThis is joi
 nt work with André Guerra (Cambridge) and João P. G. Ramos (IMPA) based 
 on the preprint:  https://arxiv.org/html/2609.07772v1\n \n\nhttps://indic
 o.math.cnrs.fr/event/16912/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/16912/
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