Phase separation on varying surfaces and convergence of diffuse interface approximations
Dienstag, 11.6.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
This talk's topic are phase separations on varying generalized hypersurfaces in\nEuclidian space. We consider a diffuse surface area (line tension) energy of Modica–\nMortola on surfaces and prove a compactness and lower bound estimate in the sharp interface\nlimit. We also consider an application to phase separated biomembranes where a Willmore energy\nfor the membranes is combined with a generalized line tension energy. For a diffuse\ndescription of such energies we give a lower bound estimate in the sharp interface limit. Time permitting I will present recent results about simultaneous phase field approximations of both the biomembrane and the indicator function for one of the two phases defined on the membrane.\n
Existence of optimal flat ribbons
Dienstag, 18.6.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We revisit the classical problem of constructing a developable surface along a given Frenet curve \(\bgamma\) in space. First, we generalize a well-known formula, introduced in the literature by Sadowsky in 1930, for the Willmore energy of the rectifying developable of \(\bgamma\) to any (infinitely narrow) flat ribbon along the same curve. Then we apply the direct method of the calculus of variations to show the existence of a flat ribbon along \(\bgamma\) having minimal bending energy. Joint work with Simon Blatt.