Geodesic
Some characterizations of a uniform ball property
Jérémy Dalphin1
1 Institut Elie Cartan of Lorraine UMR 7502, University of Lorraine BP 70239 54506 Vandoeuvre-les-Nancy Cedex, France
ESAIM. Proceedings, Tome 45 (2014), pp. 437-446.

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In 1973, Helfrich suggested a simple model to describe the shapes of vesicles: a free bending energy involving geometric quantities like curvature. However, the mathematical questions concerning the existence and the regularity of minimizers to such shape optimization problems still remain open. In this article, we consider a class of admissible shapes in which the existence of minimizers is ensured: the hypersurfaces of Rn satisfying a uniform ball condition. We prove that this property is equivalent to the notion of positive reach introduced by Federer in 1959. Then, another characterization in terms of C1,1-regularity is established for compact hypersurfaces.
DOI : 10.1051/proc/201445045

Jérémy Dalphin 1

1 Institut Elie Cartan of Lorraine UMR 7502, University of Lorraine BP 70239 54506 Vandoeuvre-les-Nancy Cedex, France 
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Jérémy Dalphin. Some characterizations of a uniform ball property. ESAIM. Proceedings, Tome 45 (2014), pp. 437-446. doi : 10.1051/proc/201445045. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445045/

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