Parametric shape optimization using the support function

The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. support function can be used in order to approximate solutions such problems by finite dimensional various constraints. We propose a framework dimensions two and three we present applications from the field convex geometry. consider depending on volume, perimeter Dirichlet Laplace eigenvalues aforementioned In particular confirm numerically Meissner’s conjecture, regarding bodies with minimal volume.