BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tobias Weth (Goethe University Frankfurt) DTSTART:20210126T180000Z DTEND:20210126T190000Z DTSTAMP:20260423T021017Z UID:OSGA/42 DESCRIPTION:Title: Cr itical domains for the first nonzero Neumann eigenvalue in Riemannian mani folds\nby Tobias Weth (Goethe University Frankfurt) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe talk is concerned with geo metric optimization problems related to the Neumann eigenvalue problem for the Laplace-Beltrami operator on bounded subdomains of a Riemannian manif old. More precisely\, we analyze locally extremal domains for the first no ntrivial eigenvalue with respect to volume preserving domain perturbation s\, and we show that corresponding notions of criticality arise in the for m of overdetermined boundary value problems. Our results rely on an extens ion of Zanger's shape derivative formula which covers the case where the f irst nonzero Neumann eigenvalue is not simple. In the second part of the t alk\, we focus on product manifolds with euclidean factors\, and we classi fy the subdomains where the associated overdetermined boundary value probl em has a solution. If time permits\, I will also briefly discuss the first nontrivial Stekloff eigenvalue. \nThis is joint work with Moustapha Fall (AIMS Senegal).\n LOCATION:https://researchseminars.org/talk/OSGA/42/ END:VEVENT END:VCALENDAR