University College London, 19th February 2019
Giovanni Catino.
“Some canonical Riemannian metrics on four manifolds: existence and rigidity”
In this talk I will present some results concerning rigidity and existence of canonical metrics on closed (compact without boundary) four manifolds. In particular I will consider Einstein metrics, Harmonic Weyl metrics and some generalizations. This is joint work with P. Mastrolia (Università degli Studi di Milano), D.D. Monticelli and F. Punzo (Politecnico di Milano).
Gilles Carron.
“Gromov-Hausdorff compactness within a conformal class”
I will talk about a recent joint work with Clara Aldana (University de Norte, Barranquilla, Colombia) and Samuel Tapie (University of Nantes, France). Let (M,g) be a a closed Riemannian manifold, I will describe what kind of compactness theorem can be obtained for conformal metrics g_f=exp(2f)g with unit volume and uniform L^{n/2} bound on the scalar curvature.
Yuxin Ge.
“Conformally compact Einstein manifolds in dimension 4”
We show some compactness result of 4-dimensional conformally compact Einstein manifolds under the suitable assumptions on the topology of the manifolds, on the compactness of their conformal infinity and on some suitable conformal invariants. We discuss also the existence and uniqueness of such manifolds when the conformal infinity is close to the standard 3-sphere. These are joint works with Alice Chang and with Alice Chang and Jie Qing.