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Mean radii of symmetrizations of a convex body
We study the relation between some successive and mean radii of a convex body and its Steiner, Schwarz, and Minkowski symmetral. In particular, we...
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On the convex hull and homothetic convex hull functions of a convex body
The aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body K in Euclidean n -sp...
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Lipschitz Selectors May Not Yield Competitive Algorithms for Convex Body Chasing
The current best algorithms for the convex body chasing (CBC) problem in online algorithms use the notion of the Steiner point of a convex set. In...
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On the Maximal Distance Between the Centers of Mass of a Planar Convex Body and Its Boundary
We prove that the length of the projection of the vector joining the centers of mass of a convex body on the plane and of its boundary to an...
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From valuations on convex bodies to convex functions
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by...
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Convex Optimization
Convex optimization or convex programming refers to the problem of minimizing convex functions over convex sets. Observe that we have been careful to...
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Chasing Convex Bodies Optimally
In the chasing convex bodies problem, an online player receives a request sequence of N convex sets...
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Morse–Smale complexes on convex polyhedra
Motivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance...
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Prescribing the gauss curvature of convex bodies in hyperbolic space
The Gauss curvature measure of a pointed Euclidean convex body is a measure on the unit sphere which extends the notion of Gauss curvature to...
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Orientation-Dependent Chord Length Distribution in a Convex Quadrilateral
AbstractThis work contributes to the research devoted to the recognition of a convex body by probabilistic characteristics of its lower-dimensional...
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On some characterizations of convex polyhedra
This work provides two sufficient conditions in terms of sections or projections for a convex body to be a polytope. These conditions are necessary...
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On star-convex bodies with rotationally invariant sections
We will prove that an origin-symmetric star-convex body K with sufficiently smooth boundary and such that every hyperplane section of K passing...
