Alan Pinoy, who has just arrived at the ULB, will speak in the geometry seminar on 14th October, at 2pm in the Salle des Profs (9th floor of building NO). Alan’s title is “Towards a positive mass theorem via the theory of potentials for asymptotically hyperbolic 3-manifolds” and his abstract is below.
The Positive Mass Theorem plays a central role in Riemannian geometry and geometric analysis. A new proof of the 3 dimensional and asymptotically flat case has been given in 2022 by Agostiniani-Mazzieri-Oronzio, making use of the theory of potentials. It relies on a new monotonicity formula holding along the level sets of the Green’s function. Recently, a notion of Volume-Renomalised Mass for asymptotically hyperbolic manifolds has been proposed by Dahl-Kröncke-McCormick, and shares a lot of properties with the usual ADM mass. In this work in progress, joint with Klaus Kröncke and Francesca Oronzio from KTH Stockholm, we aim at obtaining a similar monotonicity formula for asymptotically hyperbolic 3-manifolds in order to prove a positive mass inequality for the Volume-Renomalised Mass.