NEW INTEGRAL ESTIMATES IN SUBSTATIC MANIFOLDS AND THE ALEXANDROV THEOREM - MATTIA FOGAGNOLO (CENTRO DE GIORGI - SNS)
The classical Alexandrov Theorem in the Euclidean space asserts that any bounded set with a smooth boundary of constant mean curvature is a ball.
This result can be more quantitatively expressed by showing that an integral deficit from being of constant mean curvature dominates suitable analytic quantities that vanish exactly when the domain is a ball. In this talk, we provide generalizations of this in the context of substatic manifolds with boundary, that constitute a vast generalization of the family of manifolds with nonnegative Ricci curvature, and that are of particular importance in General Relativity. Our approach is based on the discovery of a vector field with nonnegative divergence involving the solution to a torsion-like boundary value problem introduced by Li-Xia in a related earlier work.
The talk is based on a joint work with A. Pinamonti (Trento).
Please, contact the organisers (dgseminar.torino@gmail.com) in order to get the Webex link to participate.
For more information on the seminar and on the schedule of the talks, please visit our website