Back to Search
Start Over
Li-Yau inequalities for the Helfrich functional and applications
- Source :
- Calc. Var. Partial Differential Equations 62, 45 (2023)
- Publication Year :
- 2022
-
Abstract
- We prove a general Li-Yau inequality for the Helfrich functional where the spontaneous curvature enters with a singular volume type integral. In the physically relevant cases, this term can be converted into an explicit energy threshold that guarantees embeddedness. We then apply our result to the spherical case of the variational Canham-Helfrich model. If the infimum energy is not too large, we show existence of smoothly embedded minimizers. Previously, existence of minimizers was only known in the classes of immersed bubble trees or curvature varifolds.<br />Comment: 46 Pages, 10 Figures. Fixed some typos
Details
- Database :
- arXiv
- Journal :
- Calc. Var. Partial Differential Equations 62, 45 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2203.12360
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00526-022-02381-7