Even dimensional improper affine spheres

Area Distances of Convex Plane Curves and Improper Affine Spheres

Abstract. The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane arc. Also, based ...

The Yamabe Problem on Subdomains of Even-dimensional Spheres

This problem has been extensively studied since the pioneering work of R. Schoen [10], who proved that the answer to the above question is positive when Λ consists of finitely many points (at least 2). Moreover, in the same paper, the existence of solutions to the singular Yamabe problem is proven for some sets Λ whose Hausdorff dimension is not an integer, taking away all hope to prove any reg...

Survey on Affine Spheres

Affine spheres were introduced by Ţiţeica in [72, 73], and studied later by Blaschke, Calabi, and Cheng-Yau, among others. These are hypersurfaces in affine R which are related to real Monge-Ampère equations, to projective structures on manifolds, and to the geometry of Calabi-Yau manifolds. In this survey article, we will outline the theory of affine spheres their relationships to these topics...

Affine Lines in Spheres

Because of the hairy ball theorem, the only closed 2-manifold that supports a lattice in its tangent space is T . But, if singular points (i.e. points whose tangent space is not endowed with 2 distinct coordinate directions) are allowed, then it becomes possible to give the tangent space a lattice. Because the lattice is well defined everywhere around the points, the effect of moving around the...

Affine Spheres: Discretization via Duality Relations