BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marius Müller (Albert-Ludwigs-Universität Freiburg) DTSTART:20201201T180000Z DTEND:20201201T190000Z DTSTAMP:20260423T035022Z UID:OSGA/32 DESCRIPTION:Title: Th e Willmore Flow of Tori of Revolution\nby Marius Müller (Albert-Ludwi gs-Universität Freiburg) as part of Online Seminar "Geometric Analysis"\n \n\nAbstract\nThis is a joint work with Anna Dall'Acqua\, Adrian Spener an d Reiner Schätzle. \n\nWe study the $\\textcolor{red}{\\textbf{Willmore f low}}$ of tori that have a revolution symmetry - so-called tori of revolut ion. Luckily\, the Willmore flow preserves this symmetry. Because of that we can look at the flow as an evolution of the "profile curves" - a reduct ion of the dimension!\n\nWe will examine the geometry of this curve evolut ion and understand why it is somewhat natural to look at those curves in $ \\textcolor{red}{\\textbf{hyperbolic geometry}}$. We prove: \n\n$\\textcol or{green}{ \\textbf{If the hyperbolic length of the profile curves remains bounded\, then the Willmore flow converges.}}$\n\nThe remaining question: How can the hyperbolic length of those curves be controlled? We use varia tional methods to $\\textcolor{red}{\\textbf{control the hyperbolic length }}$ by the Willmore energy - but this control is only available below an e nergy level of $\\textcolor{red}{\\mathbf{8\\pi}}$. We obtain:\n\n$\\textc olor{green}{\\textbf{If we start the Willmore flow with a torus of revolut ion of Willmore energy below $8\\pi$\, then the flow converges}.}$ \n\nIf time allows: The threshold of $8\\pi$ is also sharp and plays an important role in the context of the Willmore functional. It is also the same thres hold that was already found by E. Kuwert and R. Schätzle for the Willmore flow of spheres.\n LOCATION:https://researchseminars.org/talk/OSGA/32/ END:VEVENT END:VCALENDAR