prof. Henrot's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT
SISSA, *Tuesday, 14 July at 17.00* room 133
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Prof. Antoine Henrot
(Institut Élie Cartan - Université de Lorraine)

TITLE: Elastic energy, total mean curvature and isoperimetric inequalities

ABSTRACT:

Following L. Euler, we define the elastic energy of a planar regular 
compact set $K\subset \mathbb{R}^2$ as $E(K)=\frac{1}{2}\int_{\partial 
K} C^2 ds$ where $C$ is the curvature of the boundary. We will denote by 
$A(K)$ the area of $K$. In this talk, we investigate the problem $\min 
\{E(K), A(K)=A_0$ and prove a new isoperimetric inequality for simply 
connected domains. We also look for similar inequalities in three 
dimension where we consider the total mean curvature $\int_\Sigma H dA$ 
(where $H$ is now the mean curvature) generalizing an inequality due to 
Minkowski for some non convex domains. We give some applications for the 
minimization of the so-called Helfrich energy involved on the modelling 
of vesicles.