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SUMMARY:Fabian Rupp (Ulm University)
DTSTART:20210824T170000Z
DTEND:20210824T180000Z
DTSTAMP:20260423T021015Z
UID:OSGA/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/78/">A 
 dynamic approach to the Canham problem</a>\nby Fabian Rupp (Ulm University
 ) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nMotivated 
 by the Canham-Helfrich model for lipid bilayers\, the minimization of the 
 Willmore energy among surfaces of given topological type subject to the co
 nstraint of fixed isoperimetric ratio has been extensively studied through
 out the last decade. In this talk\, we consider a dynamical approach by in
 troducing a non-local $L^2$-gradient flow for the Willmore energy\, which 
 preserves the isoperimetric ratio. For topological spheres with initial en
 ergy below an explicit threshold\, we show global existence and convergenc
 e to a Helfrich immersion as $t\\to\\infty$. Our proof relies on a blow-up
  procedure and a constrained version of the \nŁojasiewicz--Simon gradient
  inequality.\n
LOCATION:https://researchseminars.org/talk/OSGA/78/
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