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SUMMARY:Mónica Clapp (Instituto de Matemáticas UNAM - Mexico)
DTSTART:20230519T160000Z
DTEND:20230519T170000Z
DTSTAMP:20260423T022919Z
UID:GEOTOP-A/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/43/
 ">Optimal partitions for the Yamabe equation</a>\nby Mónica Clapp (Instit
 uto de Matemáticas UNAM - Mexico) as part of GEOTOP-A seminar\n\n\nAbstra
 ct\nThe Yamabe equation on a Riemannian manifold $(M\, g)$ is of\nrelevanc
 e in differential geometry. A positive solution to it gives rise to a metr
 ic\non M which has constant scalar curvature and is conformally equivalent
  to the\ngiven metric $g$.\nAn optimal $\\ell$-partition for the Yamabe eq
 uation is a cover of M by $\\ell$-pairwise\ndisjoint open subsets such tha
 t the Yamabe equation with Dirichlet boundary\ncondition has a least energ
 y solution on each one of these sets\, and the sum of\nthe energies of the
 se solutions is minimal. Such a partition induces a generalized\nmetric th
 at vanishes on a set of measure zero and is conformally equivalent to\n$g$
  in the complement.\nI will present some results obtained in collaboration
  with Angela Pistoia\n(La Sapienza Universit`a di Roma) and Hugo Tavares (
 Universidade de Lisboa)\nthat ensure the existence and establish qualitati
 ve properties of this type of\npartitions. To do this\, we use some ideas 
 from physics.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/43/
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