Li-Yau inequalities for the Helfrich functional and applications
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916383822970880 |
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| author | Rupp, Fabian Scharrer, Christian |
| author_facet | Rupp, Fabian Scharrer, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12360 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Li-Yau inequalities for the Helfrich functional and applications Rupp, Fabian Scharrer, Christian Differential Geometry Analysis of PDEs 53C42 (primary), 49Q10, 92C10 (secondary) 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. |
| title | Li-Yau inequalities for the Helfrich functional and applications |
| topic | Differential Geometry Analysis of PDEs 53C42 (primary), 49Q10, 92C10 (secondary) |
| url | https://arxiv.org/abs/2203.12360 |