BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tuen-Wai Ng (Hong Kong University) DTSTART:20200915T130000Z DTEND:20200915T140000Z DTSTAMP:20260422T201701Z UID:CAvid/12 DESCRIPTION:Title: T he squeezing function on doubly-connected domains via the Loewner differen tial equation\nby Tuen-Wai Ng (Hong Kong University) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nInspi red by the work of Liu\, Sun and Yau (2004) on holomorphic homogeneous reg ular (HHR) domains and Yeung (2009)’s work on domains with uniform squee zing property (another name for HHR domains)\, Deng\, Guan and Zhang (2012 ) introduced a new biholomorphic invariant\, namely\, the squeezing functi on for bounded domains in the n-dimensional complex Euclidean space. Since then it has been one of the most active area in several complex variables in recent years.\n\nOn the other hand\, until now\, there is only one exp licit example of non-constant squeezing functions\, namely the squeezing f unction of the punctured ball. In this talk\, we will establish an explici t formula for the squeezing functions of annuli and hence (up to biholomor phisms) for any doubly connected planar domain. The main tools used to pro ve this result are the Schottky-Klein prime function (following the work of Crowdy) and a version of the Loewner differential equation on annuli du e to Komatu. We will also show that these results can be used to obtain lo wer bounds on the squeezing function for certain product domains in the n- dimensional complex Euclidean space.\n\nThis is a joint work with Chiu Cha k Tang and Jonathan Tsai.\n LOCATION:https://researchseminars.org/talk/CAvid/12/ END:VEVENT END:VCALENDAR