6 citations · 13 across the 13 of their papers we have counts for
22 papers
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…
A new geometric viewpoint on Sturm-Liouville eigenvalue problems
Vitor Balestro, Horst Martini, Ralph Teixeira
In Euclidean plane geometry, cycloids are curves which are homothetic to their respective bi-evolutes. In smooth normed planes, cycloids can be similarly defined, and they are char…
On curvature of surfaces immersed in normed spaces
Vitor Balestro, Horst Martini, Ralph Teixeira
The normal map given by Birkhoff orthogonality yields extensions of principal, Gaussian and mean curvatures to surfaces immersed in three-dimensional spaces whose geometry is given…
Some topics in differential geometry of normed spaces
Vitor Balestro, Horst Martini, Ralph Teixeira
For a surface immersed in a three-dimensional space endowed with a norm instead of an inner product, one can define analogous concepts of curvature and metric. With these concepts…