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SUMMARY:Eigenvalue optimization in higher dimensions and p-harmonic maps -
  Denis Vinokurov (Université de Montréal)
DTSTART:20260204T121500Z
DTEND:20260204T124500Z
UID:TALK239812@talks.cam.ac.uk
DESCRIPTION:We will discuss the existence of metrics on a closed Riemannia
 n manifold of dimensionm &ge\; 3 that maximize the kth Laplace eigenvalue 
 within a conformal class. Previously\,such existence results were known on
 ly in dimension two. More generally\, we consider afamily of eigenvalue op
 timization problems parametrized by the choice of normalization.\nThe crit
 ical points of the resulting normalized eigenvalue functionals are related
  top-harmonic maps into spheres\, where 2 &le\; p &le\; m\, with the case 
 p = m correspondingto optimization within a conformal class. A key tool in
  the analysis is the use oftechniques from the theory of topological tenso
 r products\, which appear to be well suitedfor studying eigenvalue optimiz
 ation problems.
LOCATION:Seminar Room 1\, Newton Institute
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