151 citations · 408 across the 36 of their papers we have counts for
47 papers
On the number of antipodal or strictly antipodal pairs of points in finite subsets of , III
E. Makai, H. Martini, M. H. Nguyên +2
We improve our earlier upper bound on the numbers of antipodal pairs of points among points in , to , for some . We prove that the minimal n…
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…
Differential geometry of spatial curves for gauges
Vitor Balestro, Horst Martini, Makoto Sakaki
We derive Frenet-type results and invariants of spatial curves immersed in -dimensional generalized Minkowski spaces, i.e., in linear spaces which satisfy all axioms of finite d…
Curvature types of planar curves for gauges
Vitor Balestro, Horst Martini, Makoto Sakaki
In this paper results from the differential geometry of curves are extended from normed planes to gauge planes which are obtained by neglecting the symmetry axiom. Based on the gau…
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…