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Seminários do IMPA

Geometria Diferencial

Higher Willmore energies, Q-curvatures, and related global geometry problems.
Rod Gover

University of Auckland
Terça-feira, 2 de abril de 2019, 15:30
Sala 236.


  The Willmore energy and its functional gradient (under variations of
  embedding) have recently been the subject of recent interest in both
  geometric analysis and physics, in part because of their link to
  conformal geometry. Considering a singular Yamabe problem on manifolds
  with boundary shows that these these surface invariants are the lowest
  dimensional examples in a family of conformal invariants for
  hypersurfaces in any dimension. The same construction and variational
  considerations shows that (on even dimensional hypersurfaces) the
  higher Willmore energy and its functional gradient are analogues of
  the integral of the celebrated Q-curvature conformal invariant and its
  function gradient (now with respect to metric variations) which is
  known as the Fefferman-Graham obstruction tensor (or the Bach tensor
  in dimension 4). In fact the link is deeper than this in that the
  Willmore energy we consider is an integral of an invariant that actually
  generalises the Branson Q-curvature. This is part of fascinating
  unifying picture that includes some interesting open problems in
  global geometry.