Yamabe flow and minimal entropy
The entropy is a geometric invariant of Riemannian manifolds which comes from dynamic. When the curvature is negative, a minimum of the entropy is believed to detect a maximum of symmetry. I will present a version of the Yamabe flow, from which we show that in a conformal class of a metric with negative curvature, the minimum of the entropy is reached by the unique metric with constant scalar curvature. [joint work with P. Suarez-Serrato, MPIM Bonn]