BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Azahara DelaTorre (Sapienza Università di Roma) DTSTART:20220222T170000Z DTEND:20220222T180000Z DTSTAMP:20260423T052333Z UID:OSGA/97 DESCRIPTION:Title: Th e fractional Yamabe problem with singularities\nby Azahara DelaTorre ( Sapienza Università di Roma) as part of Online Seminar "Geometric Analysi s"\n\n\nAbstract\nThe so called Yamabe problem in Conformal Geometry consi sts in finding a metric conformal to a given one and which has constant sc alar curvature. From the analytic point of view\, this problem becomes a s emilinear elliptic PDE with critical (for the Sobolev embedding) power non -linearity. If we study the problem in the Euclidean space\, allowing the presence of nonzero-dimensional singularities can be transformed into redu cing the non-linearity to a Sobolev-subcritical power. A quite recent noti on of non-local curvature gives rise to a parallel study which weakens the geometric assumptions giving rise to a non-local semilinear elliptic PDE. \n\nIn this talk\, we will focus on metrics which are singular along nonz ero-dimensional singularities. In collaboration with Ao\, Chan\, Fontelos\ , González and Wei\, we covered the construction of solutions which are s ingular along (zero and positive dimensional) smooth submanifolds in this fractional setting. This was done through the development of new methods c oming from conformal geometry and Scattering theory for the study of non-l ocal ODEs. Due to the limitations of the techniques we used\, the particul ar case of ``maximal’’ dimension for the singularity was not covered. In a recent work\, in collaboration with H. Chan\, we cover this specific dimension constructing and studying singular solutions of critical dimensi on.\n LOCATION:https://researchseminars.org/talk/OSGA/97/ END:VEVENT END:VCALENDAR