# A formal Riemannian structure on the space of conformal metrics and some applications.

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Matthew Gursky

created by malchiodi on 06 May 2016

18 may 2016
-- 16:00
[open in google calendar]

Scuola Normale Superiore, Aula Tonelli

**Abstract.**

In this talk I will present some results from project with J. Streets (UC-Irvine), in which we define a formal
Riemannian metric on the set of metrics in a conformal class with positive (or negative) curvature. In the case of surfaces,
this metric has many interesting formal properties; for example the curvature is nonpositive and the Liouville energy is geodesically convex.
I will then talk about extensions to higher dimensions, especially 4-d, in which this construction has some interesting applications
to the fully nonlinear Yamabe problem.