BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mattia Fogagnolo (Centro De Giorgi - SNS) DTSTART:20220322T150000Z DTEND:20220322T160000Z DTSTAMP:20260423T052954Z UID:DGSTO/28 DESCRIPTION:Title: N ew integral estimates in substatic manifolds and the Alexandrov Theorem\nby Mattia Fogagnolo (Centro De Giorgi - SNS) as part of Differential Ge ometry Seminar Torino\n\n\nAbstract\nThe classical Alexandrov Theorem in t he Euclidean space asserts that any bounded set with a smooth boundary of constant mean curvature is a ball.\nThis result can be more quantitatively expressed by showing that an integral deficit from being of constant mea n curvature dominates suitable analytic quantities that vanish exactly whe n the domain is a ball. In this talk\, we provide generalizations of this in the context of substatic manifolds with boundary\, that constitute a va st generalization of the family of manifolds with nonnegative Ricci curvat ure\, and that are of particular importance in General Relativity. Our app roach is based on the discovery of a vector field with nonnegative diverge nce involving the solution to a torsion-like boundary value problem introd uced by Li-Xia in a related earlier work.\nThe talk is based on a joint wo rk with A. Pinamonti (Trento).\n LOCATION:https://researchseminars.org/talk/DGSTO/28/ END:VEVENT END:VCALENDAR