BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Salvatore Stuvard (University of Milan) DTSTART:20260318T093000Z DTEND:20260318T113000Z DTSTAMP:20260423T005831Z UID:NCTS-GMT/34 DESCRIPTION:Title: The epsilon-regularity theorem for Brakke flows near triple junctions\nby Salvatore Stuvard (University of Milan) as part of NCTS internationa l Geometric Measure Theory seminar\n\n\nAbstract\nIn a pioneering paper pu blished on JDG in 1993\, Leon Simon\nestablished a powerful method to demo nstrate\, among other things\, the validity of\nthe following result: if a multiplicity one minimal $k$-dimensional surface (stationary\nvarifold) i s sufficiently close\, in the unit ball and in a weak measure-theoretic\ns ense\, to the stationary cone given by the union of three $k$-dimensional half-planes\nmeeting along a $(k-1)$-dimensional subspace and forming angl es of 120 degrees\nwith one another\, then\, in a smaller ball\, the surfa ce must be a $C^{1\,\\alpha}$\ndeformation of the cone. In this talk\, I w ill present the proof of a parabolic\ncounterpart of this result\, which a pplies to general classes of (possibly forced)\nweak mean curvature flows (Brakke flows). I will particularly focus on the need of\nan assumption\, which is absent in the elliptic case\, and which\, on the other hand\,\nis satisfied by both Brakke flows with multi-phase grain boundaries structur e and\nby Brakke flows that are flows of currents mod 3: these are the mai n classes of\nBrakke flows for which a satisfactory existence theory is cu rrently available and\ntriple junction singularities are expected. In thes e cases\, the theorem holds true\nunconditionally\, and it implies uniquen ess of multiplicity-one\, backward-static triple\njunctions as tangent flo ws as well as a structure theorem on the singular set under\nsuitable Gaus sian density restrictions.\nThis is a joint work with Yoshihiro Tonegawa ( Institute of Science Tokyo).\n LOCATION:https://researchseminars.org/talk/NCTS-GMT/34/ END:VEVENT END:VCALENDAR