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UID:20250704T185315EDT-4168c8PuLM@132.216.98.100
DTSTAMP:20250704T225315Z
DESCRIPTION:Abstract: The first subject of this talk is an isoperimetric ine
 quality for the second non-zero eigenvalue of the Laplace-Beltrami operato
 r on the real projective plane (based on a joint paper with N. Nadirashvil
 i). For a metric of area 1 this eigenvalue is not greater than 20\pi. This
  value could be attained as a limit on a sequence of metrics of area 1 on 
 the projective plane converging to a singular metric on the projective pla
 ne and the sphere with standard metrics touching in a point such that the 
 ratio of the areas of the projective plane and the sphere is 3:2. The seco
 nd subject of this talk is a very recent result (joint paper with M. Karpu
 khin\, N. Nadirashvili and I. Polterovich) about an isoperimetric inequali
 ty for Laplace eigenvalues on the sphere. For a metric of area 1 the k-th 
 eigenvalue is not greater than 8\pi k. This value could be attained as a l
 imit on a sequence of metrics of area 1 on the sphere converging to a sing
 ular metric on k spheres with standard metrics of equal radius touching in
  a point.\n
DTSTART:20170828T173000Z
DTEND:20170828T183000Z
LOCATION:Room 5183\, CA\, University de Montreal
SUMMARY:Alexei Penskoi (Moscow State University and Higher School of Econom
 ics)
URL:/mathstat/channels/event/alexei-penskoi-moscow-sta
 te-university-and-higher-school-economics-269574
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