**Clique Aqui!**

Seminários do IMPA

Geometria Diferencial

Título |
Higher Willmore energies, Q-curvatures, and related global geometry problems. |

Expositor |
Rod Gover
University of Auckland |

Data |
Terça-feira, 2 de abril de 2019, 15:30 |

Local |
Sala 236. |

Resumo |

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.