BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Oliver Roth (University of Würzburg) DTSTART:20210504T130000Z DTEND:20210504T140000Z DTSTAMP:20260422T200946Z UID:CAvid/39 DESCRIPTION:Title: A new Schwarz-Pick Lemma at the boundary and rigidity of holomorphic maps\nby Oliver Roth (University of Würzburg) as part of CAvid: Complex Ana lysis video seminar\n\nLecture held in N/A.\n\nAbstract\nWe establish seve ral invariant boundary versions of the (infinitesimal) Schwarz-Pick lemma for conformal pseudometrics on the unit disk and for holomorphic selfmaps of strongly convex domains in CN in the spirit of the boundary Schwarz lem ma of Burns-Krantz. Firstly\, we focus on the case of the unit disk and pr ove a general boundary rigidity theorem for conformal pseudometrics with v ariable curvature. In its simplest cases this result already includes new types of boundary versions of the lemmas of Schwarz-Pick\, Ahlfors-Schwarz and Nehari-Schwarz. The proof is based on a new Harnack-type inequality a s well as a boundary Hopf lemma for conformal pseudometrics which extend e arlier interior rigidity results of Golusin\, Heins\, Beardon\, Minda and others. Secondly\, we prove similar rigidity theorems for sequences of con formal pseudometrics\, which even in the interior case appear to be new. F or instance\, a first sequential version of the strong form of Ahlfors' le mma is obtained. As an auxiliary tool we establish a Hurwitz-type result a bout preservation of zeros of sequences of conformal pseudometrics. Thirdl y\, we apply the one-dimensional sequential boundary rigidity results toge ther with a variety of techniques from several complex variables to prove a boundary version of the Schwarz-Pick lemma for holomorphic maps of stron gly convex domains in $\\C^N$ for $N>1$.\n\n(This is joint work with Filip po Bracci and Daniela Kraus)\n LOCATION:https://researchseminars.org/talk/CAvid/39/ END:VEVENT END:VCALENDAR