Conference Agenda
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Daily Overview |
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Gvp2: Geometric variational problems Location: A704 Session Chair: Fabian Rupp Session Chair: Christian Scharrer | |
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Asymptotic analysis of Willmore flows with boundary: Overview and Outlook Salzburg University, Germany The Willmore flow is a fourth-order quasi-linear degenerate-parabolic system, with the structure of an $L^2$-gradient flow for the Willmore energy of surfaces. The talk’s focus is the study of boundary value problems. I’ll first review results known for closed surfaces: local existence and (geometric) uniqueness for low-regularity initial data, stability near local minimizers via a \L ojasiewicz-Simon-gradient inequality, and the analysis of the long-time behavior based on controlling local $L^2$-concentrations of curvature. Then I’ll point out difficulties when adapting these to boundary problems, explain how these are addressed in recent results, and close with an outlook on future work. | |
