Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference45 articles.
1. Alexandrov, A.D.: A characteristic property of spheres. Ann. Mat. Pura Appl. 4(58), 303–315 (1962)
2. Allard, W.K.: On the first variation of a varifold. Ann. Math. 2(95), 417–491 (1972)
3. Ambrosio, L., Caselles, V., Masnou, S., Morel, J.-M.: Connected components of sets of finite perimeter and applications to image processing. J. Eur. Math. Soc. (JEMS) 3(1), 39–92 (2001)
4. Bellettini, C., Wickramasekera, N.: The inhomogeneous Allen–Cahn equation and the existence of prescribed-mean-curvature hypersurfaces (2020)
5. Bernard, Y., Wheeler, G., Wheeler, V.-M.: Rigidity and stability of spheres in the Helfrich model. Interfaces Free Bound. 19(4), 495–523 (2017)
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