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Extreme problems for convex curves with given relative Chebyshev radius
Vitor Balestro, Horst Martini, Yurii Nikonorov +1
The paper is devoted to some extremal problems for convex curves and polygons in the Euclidean plane referring to the relative Chebyshev radius. In particular, we determine the rel…
Convex analysis in normed spaces and metric projections onto convex bodies
Vitor Balestro, Horst Martini, Ralph Teixeira
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual…
Asymmetry measures for convex distance functions
Vitor Balestro, Horst Martini, Ralph Teixeira
Gauges, or convex distance functions are, roughly speaking, norms without symmetry. In this paper we intend to quantify how asymmetric a planar gauge can be. We introduce asymmetry…
Duality of gauges and symplectic forms in vector spaces
Vitor Balestro, Horst Martini, Ralph Teixeira
A gauge in a vector space is a distance function given by the Minkowski functional associated to a convex body containing the origin in its interior. Thus, the outcomin…
The Rosenthal-Szasz inequality for normed planes
Vitor Balestro, Horst Martini
We aim to study the classical Rosenthal-Szasz inequality for a plane whose geometry is given by a norm. This inequality states that the bodies of constant width have the largest pe…
Angle measures, general rotations, and roulettes in normed planes
Vitor Balestro, Ákos G. Horváth, Horst Martini
In this paper a special group of bijective maps of a normed plane, called the group of general rotations, is introduced; it contains the isometry group as a subgroup. The concept o…