Ge: Compactness of asymptotically hyperbolic Einstein 4-manifolds

Ge: The seminar is in presence. Please write to 
andrea.malchiodi@sns.it if you want to attend online via Teams
Let $X^4$ be a differenntial 4-manifold with boundary $M^3 = \partial X^4$. Given the conformal
class $(M, [h])$ of a Riemannian metric $h$ on $M$, we try to find ”conformal filling in” a asymptot-
ically hyperbolic Einstein $g_+$ on $X$ such that $r^2 g_{+}\mid_{M} = h$ for some defining function $r$ on $X$. The study of complete AH Einstein manifolds has become very active due to the $AdS/CFT$ correspondence in string theory.In this talk, instead of addressing the existence problem of a conformal filling in, we discuss
the compactness problem, that is, how the compactness of the sequence of conformal infinity
metrics leads to the compactness result of the compactified filling in AHE manifolds under
the suitable assumptions on the topology of $X$ and some conformal invariants. We briefly
survey some known results then report recent joint work in progress with Alice Chang. Some
applications will be discussed.
http://cvgmt.sns.it/seminar/870/

When	Fri Jun 3, 2022 9am – 10am Coordinated Universal Time
Where	Aula Volterra (map)