Estimating the diameter of the space of planar convex figures with respect to an affine-invariant metric.
Étude des différences de corps convexes plans
We characterize the linear space ℋ of differences of support functions of convex bodies of 𝔼² and we consider every h ∈ ℋ as the support function of a generalized hedgehog (a rectifiable closed curve having exactly one oriented support line in each direction). The mixed area (for plane convex bodies identified with their support functions) has a symmetric bilinear extension to ℋ which can be interpreted as a mixed area for generalized hedgehogs. We study generalized hedgehogs and we extend the...
Euclidean arrangements in Banach spaces
We study the way in which the Euclidean subspaces of a Banach space fit together, somewhat in the spirit of the Kashin decomposition. The main tool that we introduce is an estimate regarding the convex hull of a convex body in John's position with a Euclidean ball of a given radius, which leads to a new and simplified proof of the randomized isomorphic Dvoretzky theorem. Our results also include a characterization of spaces with nontrivial cotype in terms of arrangements of Euclidean subspaces.
Euclidean Convexity Cannot be Compactified.
Euclidean Number Fields of Large Degree
Euclidean perimeter of classes of optimal convex lattice -gons.
Eulers Charakteristik und die Beschränktheit konvexer Polyeder.
Euler's Polyhedron Formula
Euler's polyhedron theorem states for a polyhedron p, thatV - E + F = 2,where V, E, and F are, respectively, the number of vertices, edges, and faces of p. The formula was first stated in print by Euler in 1758 [11]. The proof given here is based on Poincaré's linear algebraic proof, stated in [17] (with a corrected proof in [18]), as adapted by Imre Lakatos in the latter's Proofs and Refutations [15].As is well known, Euler's formula is not true for all polyhedra. The condition on polyhedra considered...
Eulersche Charakteristik, Projektionen und Quermaßintegrale.
Even astral configurations.
Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature
We relate the total curvature and the isoperimetric deficit of a curve in a two-dimensional space of constant curvature with the area enclosed by the evolute of . We provide also a Gauss-Bonnet theorem for a special class of evolutes.
Examples of convex functions and classifications of normed spaces.
Existence et unicité du maximum d'une forme linéaire sur un ensemble de matrices diagonales
Existence of open quasiconvex subsets dense in a given space
Existence theorems for some optimal control problems
Expectation and variance of the volume covered by a large number of independent random sets
Expectation of Random Polytopes.
Explicit Ramsey graphs and Erdős distance problems over finite Euclidean and non-Euclidean spaces.
Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact
We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.
Extendable Shelling, Simplicial and Toric h-vector of Some Polytopes