151 citations · 408 across the 36 of their papers we have counts for
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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…
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…