BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Luís Alías (Universidad de Murcia) DTSTART:20201029T190000Z DTEND:20201029T200000Z DTSTAMP:20260423T052954Z UID:UFPB/12 DESCRIPTION:Title: Tr apped submanifolds into the light cone\nby Luís Alías (Universidad d e Murcia) as part of Seminários de Matemática da UFPB\n\n\nAbstract\nThe concept of trapped surfaces was originally formulated by Penrose in his s eminal paper published in 1965\, very recently laureated with the Nobel Pr ize in Physics 2020. In that paper Penrose introduced 2-dimensional trappe d surfaces in 4-dimensional spacetimes in terms of the signs or the vanish ing of the so-called null expansions. This is obviously related to the cau sal orientation of the mean curvature vector of the surface\, which provid es a better and powerful characterization of the trapped surfaces and allo ws the generalization of this concept to codimension two spacelike submani folds of arbitrary dimension. \n\nIn this lecture we consider codimension two trapped submanifolds contained into the light cone of de Sitter spacet ime and into the light cone of the Lorentz-Minkowski spacetime. In particu lar\, for the case of compact submanifolds into the light cone of de Sitte r space\, we show that they are conformally diffeomorphic to the round sph ere. This fact enables us to deduce that the problem of characterizing com pact marginally trapped submanifolds into the light cone is equivalent to solving the Yamabe problem on the round sphere\, allowing us to obtain our main classification result for such submanifolds. As for the case of subm anifolds into the light cone of the Lorentz-Minkowski space\, we obtain a non-existence result for complete\, non-compact\, weakly trapped submanifo lds.\n\nThese results have been obtained in collaboration with Verónica L . Cánovas (from Universidad de Murcia) and Marco Rigoli (from Università degli Studi di Milano)\, and they can be found in the following papers: T rapped submanifolds contained into a null hypersurface of de Sitter spacet ime\, Commun. Contemp. Math. 20 (2018)\, no. 8\, 1750059\, 30 pp.\; and Co dimension two spacelike submanifolds of the Lorentz-Minkowski spacetime in to the light cone\, Proc. Roy. Soc. Edinburgh Sect. A 149 (2019)\, no. 6\, 1523-1553.\n LOCATION:https://researchseminars.org/talk/UFPB/12/ END:VEVENT END:VCALENDAR