Hedgehogs of constant width and equichordal points
We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.
Hidden structures in the class of convex functions and a new duality transform
Our main intention in this paper is to demonstrate how some seemingly purely geometric notions can be presented and understood in an analytic language of inequalities and then, with this understanding, can be defined for classes of functions and reveal new and hidden structures in these classes. One main example which we discovered is a new duality transform for convex non-negative functions on attaining the value 0 at the origin (which we call “geometric convex functions”). This transform, together...
Hyperplane conjecture for quotient spaces of Lp.
Hyperplane sections of convex bodies in isotropic position.
Illumination and visibility problems in terms of closure operators.
Improved Bounds on Weak e-Nets for Convex Sets.
Indice d'un hérisson: étude et applications.
Hedgehogs are a natural generalization of convex bodies of class C+2. After recalling some basic facts concerning this generalization, we use the notion of index to study differential and integral geometries of hedgehogs.As applications, we prove a particular case of the Tennis Ball Theorem and a property of normals to a plane convex body of constant width.
Inequalities Between Intrinsic Volumes.
Inequalities for general width-integrals of Blaschke-Minkowski homomorphisms
We establish some inequalities for general width-integrals of Blaschke-Minkowski homomorphisms. As applications, inequalities for width-integrals of projection bodies are derived.
Inequalities for radial Blaschke-Minkowski homomorphisms
We establish Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms, which in special cases yield some new results for intersection bodies. Moreover, we obtain two monotonicity inequalities for radial Blaschke-Minkowski homomorphisms.
Inequalities of the Kahane-Khinchin type and sections of -balls
We extend Kahane-Khinchin type inequalities to the case p > -2. As an application we verify the slicing problem for the unit balls of finite-dimensional spaces that embed in , p > -2.
Inner and Outer j-Radii of Convex Bodies in Finite-Dimensional Normed Spaces.
Inradius und Dicke konvexer Körper aus optimierungstheoretischer Sicht
Interior Points of the Convex Hull of Few Points in ...
Invariant convex sets and functions in Lie algebras.
Isometrien des Konvexringes
Isometrien des Raumes der konvexen Körper
Isometries of Spaces of Compact Convex Subsets of Metric Manifolds.
Isoperimetric inequalities and identifties for k-dimensional cross-sections of convex bodies.
Isoperimetrische Ungleichungen für geschlossene Kurven