prof. Bour's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT


Prof. Vincent Bour
(Université de Nantes)


Title : Fourth order curvature flows and geometric applications.

Abstract : We present a proof of a rigidity result for compact four
manifolds that is entirely based on a geometric flow. To achieve this
goal, we study the gradient flows of a number of quadratic curvature
functionals on four manifolds. We show that if the flow starts with a
metric of positive Yamabe constant and if we assume an explicit bound on
the initial energy, then no singularity can occur. Under those
assumptions, the flow exists for all time, and converges to a quotient of
the sphere. It gives an alternative proof, under stronger assumptions, of
a theorem of A. Chang, M. Gursky and P. Yang asserting that integral
pinched four manifolds with positive Yamabe constant are space forms.


Thursday 20 December at 14.00 in lecture room 133