Calculus of Variations and Geometric Measure Theory

A. Kubin - L. Lussardi - M. Morandotti

Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs

created by morandott on 19 Jan 2022
modified by lussardi on 11 Mar 2024


Published Paper

Inserted: 19 jan 2022
Last Updated: 11 mar 2024

Journal: J. Geom. Anal.
Volume: 34
Number: 121
Pages: 1-25
Year: 2024

ArXiv: 2201.06353 PDF


The existence of minimizers of the Canham-Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham-Helfrich functional, usually defined on regular surfaces, is extended to generalized Gauss graphs, then lower semicontinuity and compactness are proved under a suitable condition on the bending constants ensuring coerciveness; the minimization follows by the direct methods of the Calculus of Variations. Remarks on the regularity of minimizers and on the behavior of the functional in case there is lack of coerciveness are presented.