The Euler-Helfrich Functional (2107.12500v1)

Published 26 Jul 2021 in math.DG and math.AP

Abstract: We investigate equilibrium configurations for surface energies which contain the squared $L^2$ norm of the difference of the mean curvature H and the spontaneous curvature $c_o$ coupled with the elastic energy of the boundary curve, which we studied previously in [23]. It is shown that if a critical surface for this type of functional is axially symmetric, then it satisfies a simpler second order variational problem. Many examples of solutions of this are given.

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (2)

Collections

Sign up for free to add this paper to one or more collections.