BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francesco Bonsante (Università degli Studi di Pavia) DTSTART:20210127T160000Z DTEND:20210127T170000Z DTSTAMP:20260423T035816Z UID:DGSTO/8 DESCRIPTION:Title: Mi nimizing immersions of surfaces in hyperbolic 3-manifolds\nby Francesc o Bonsante (Università degli Studi di Pavia) as part of Differential Geom etry Seminar Torino\n\n\nAbstract\nTrapani and Valle proposed to study the L^1 holomorphic energy of diffeomorphisms between Riemannian surfaces. Th is is defined as the L^1-norm of the (1\,0)-part of the differential of th e map. They proved that if the domain and the target are surfaces of negat ive curvature\, any homotopy class of diffeomorphisms contains a unique mi nimizer for the functional. In a recent work with Gabriele Mondello and Je an-Marc Schlenker we tried to generalize the functional in the setting wh ere the domain is a hyperbolic surface and the target a hyperbolic 3-manif old. The functional here is the L^1-Shatten energy\, which in fact coincid es with the L^1-holomorphic energy in the 2-dimensional case. More concret ely we considered the space of equivariant maps of the universal covering of a fixed surface of genus g into the hyperbolic space\, and studied map s which minimize the L^1-Shatten energy on fibers of the monodromy map. We proved that the space of such minimizing maps is naturally a complex mani fold of dimension 6g-6\, where g is the genus of the surface\, so that the monodromy map realize a holomorphic embedding onto some open subset of th e PSL_2(C)-character variety containing the Fuchsian locus.\n\nIn the talk I will describe the main results of this joint work.\n LOCATION:https://researchseminars.org/talk/DGSTO/8/ END:VEVENT END:VCALENDAR