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Philipp Reiter (University of Georgia)
Location: Hill 705
Date & time: Tuesday, 18 September 2018 at 3:00PM - 4:00PM
Abstract: During the last thirty years, several (families of) functionals have been defined that model self-avoidance: their values tend to infinity if an embedded object degenerates, e.g., if a sequence of closed simple curves converges to a curve with a self-intersection. Many of these functionals exhibit regularizing effects: they do not only ensure embeddedness but in fact constitute some sort of 'curvature measure'. In several cases the first variation turns out to be an elliptic pseudo-differential operator which under certain conditions permits to derive smoothness of critical points. On the other hand, repulsive functionals can be used to model impermeability of elastic objects, for instance they can be applied to the evolution of inextensible curves subject to the elastic flow.