We use the intrinsic area to define a distance on space of homothety classes convex bodies in $n$-dimensional Euclidean space, which makes it isometric subset infinite dimensional hyperbolic space. The ambient Lorentzian structure is an extension form bodies, and Alexandrov–Fenchel inequality interpreted as reversed Cauchy–Schwarz inequality. deduce that similarity has proper geodesic with curv...

The convex dimension of a graph G = (V, E) is the smallest dimension d for which G admits an injective map f : V −→ R of its vertices into d-space, such that the barycenters of the images of the edges of G are in convex position. The strong convex dimension of G is the smallest d for which G admits a map as above such that the images of the vertices of G are also in convex position. In this pap...

We provide an explicit resolution of the Abreu equation on convex labeled quadrilaterals. This confirms a conjecture of Donaldson in this particular case and implies a complete classification of the explicit toric Kähler– Einstein and toric Sasaki–Einstein metrics constructed in [6, 23, 14]. As a byproduct, we obtain a wealth of extremal toric (complex) orbi-surfaces, including Kähler–Einstein ...

The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight frame. In this paper we define m-scalability, a refinement of scalability based on the number of nonzero weights used in the rescaling process, and study the connection between this notion and ele...

(in alphabetic order by speaker surname) Speaker: Judit Abardia (Frankfurt University) Title: Projection bodies in complex vector spaces Abstract: The projection body of a convex body in the Euclidean space was characterized by Monika Ludwig as the unique Minkowski valuation which is continuous, translation invariant and contravariant under the (real) special linear group. In a joint work with ...