Direct minimization of the Canham–Helfrich energy on generalized Gauss graphs
speaker: Anna Kubin (Politecnico di Torino)abstract: Given a smooth two-dimensional manifold $M$ oriented by a unit normal field $\nu$, the Gauss graph of $M$ is the graph of the Gauss map $\nu$. Exploiting the fact that the curvatures of $M$ are coded in its Gauss map, Anzellotti, Serapioni and Tamanini 2 generalized the notion of Gauss graph of a manifold and developed the theory of generalized Gauss graphs.In 1 we prove the existence of minimizers of the Canham--Helfrich functional in the setting of generalized Gauss graphs. As a first step, we extendthe Canham--Helfrich functional, usually defined on regular surfaces, to generalized Gauss graphs, then we prove lower semicontinuity and compactness undera suitable condition on the bending constants ensuring coerciveness; the minimization follows by the direct methods of the Calculus of Variations. Finally, we present remarks on the regularity of minimizers and on the behavior of thefunctional in case there is lack of coerciveness.
References 1 A. Kubin, L. Lussardi and M. Morandotti, Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs, preprint 2022. 2 G. Anzellotti, R. Serapioni and I. Tamanini, Curvatures, functionals, currents, Indiana Univ. Math. J., 39(3):617-669, 1990.
timetable:
Wed 14 Sep, 17:30 - 18:30, Aula Dini
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