2 research outputs found
Uniform ball property and existence of optimal shapes for a wide class of geometric functionals
In this paper, we are interested in shape optimization problems involving the
ge ometry (normal, curvatures) of the surfaces. We consider a class of
hypersurface s in satisfying a uniform ball condition and we
prove the exist ence of a -regular minimizer for general geometric
functionals and cons traints involving the first- and second-order properties
of surfaces, such as in problems of the form:
where , , and respectively denotes the
normal, the scalar mea n curvature and the Gaussian curvature. We gives some
various applications in th e modelling of red blood cells such as the
Canham-Helfrich energy and the Willmo re functional