Existence of varifold minimizers for the multiphase Canham-Helfrich\n functional

2019/12/03 by Katharina Brazda, Brazda, Katharina, Luca Lussardi +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Medicine · #49J45 #49Q10 #49Q20 #53C80 #92C10 #Analysis of PDEs (math.AP) #Biological Physics (physics.bio-ph) #Cell Adhesion Molecules Research #Cellular Mechanics and Interactions #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1912.02614

openalex publication_date 2019/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the minimization of the Canham-Helfrich functional in presence of\nmultiple phases. The problem is inspired by the modelization of heterogeneous\nbiological membranes, which may feature variable bending rigidities and\nspontaneous curvatures. With respect to previous contributions, no symmetry of\nthe minimizers is here assumed. Correspondingly, the problem is reformulated\nand solved in the weaker frame of oriented curvature varifolds. We present a\nlower semicontinuity result and prove existence of single- and multiphase\nminimizers under area and enclosed-volume constrains. Additionally, we discuss\nregularity of minimizers and establish lower and upper diameter bounds.\n

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