Affine classification of -curves.
A family of regular annuli is considered. Affine invariants of annuli are introduced.
This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss affine Bernstein problems and complete constant mean curvature surfaces in equiaffine differential geometry.
We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.
The classical medial axis and symmetry set of a smooth simple plane curve M, depending as they do on circles bitangent to M, are invariant under euclidean transformations. This article surveys the various ways in which the construction has been adapted to be invariant under affine transformations. They include affine distance and area constructions, and also the 'centre symmetry set' which generalizes central symmetry. A connexion is also made with the tricentre set of a convex plane curve, which...