Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Vitor Balestro"'
Publikováno v:
Advances in Geometry. 21:109-118
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 in mind, various questions immediately appear. The aim of this paper i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b1dded71f800efd83377d835322f87b7
https://doi.org/10.1515/advgeom-2020-0001
https://doi.org/10.1515/advgeom-2020-0001
Autor:
Vitor Balestro, Horst Martini
Publikováno v:
Surveys in Geometry I ISBN: 9783030866945
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::67804868cbb0c7454056e2f9a299f392
https://doi.org/10.1007/978-3-030-86695-2_3
https://doi.org/10.1007/978-3-030-86695-2_3
Publikováno v:
Expositiones Mathematicae. 37:347-381
The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a comprehensive overview
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::05caa524117e25ee986460fe4fd9b026
https://doi.org/10.1016/j.exmath.2018.04.002
https://doi.org/10.1016/j.exmath.2018.04.002
Publikováno v:
Analysis and Mathematical Physics. 9:2413-2434
We investigate an inverse problem referring to roulettes in normed planes, thus generalizing analogous results of Bloom and Whitt on the Euclidean subcase. More precisely, we prove that a given curve can be traced by rolling another curve along a lin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6600f83983d06c25fb53505c0ce0f610
https://doi.org/10.1007/s13324-019-00343-5
https://doi.org/10.1007/s13324-019-00343-5
Publikováno v:
Monatshefte für Mathematik. 190:213-236
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 characterized by their radius of curvature functions being solutions to ei
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c8e51d1f2d9530cdd4970a78fc8bc5f0
https://doi.org/10.1007/s00605-019-01291-9
https://doi.org/10.1007/s00605-019-01291-9
Publikováno v:
Results in Mathematics. 76
The paper is devoted to some extremal problems for convex curves and polygons in the Euclidean plane referring to the self Chebyshev radius. In particular, we determine the self Chebyshev radius for the boundary of an arbitrary triangle. Moreover, we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::38153fa4df777f6c1b1cef173e734c76
https://doi.org/10.1007/s00025-021-01394-6
https://doi.org/10.1007/s00025-021-01394-6
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced
We derive Frenet-type results and invariants of spatial curves immersed in $3$-dimensional generalized Minkowski spaces, i.e., in linear spaces which satisfy all axioms of finite dimensional real Banach spaces except for the symmetry axiom. Further o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c914d9b00f0b306622ae2785d70ab2a6
http://arxiv.org/abs/2001.01379
http://arxiv.org/abs/2001.01379
Autor:
Horst Martini, Vitor Balestro
Publikováno v:
Bulletin of the Australian Mathematical Society. 99:130-136
We study the classical Rosenthal–Szasz inequality for a plane whose geometry is determined by a norm. This inequality states that the bodies of constant width have the largest perimeter among all planar convex bodies of given diameter. In the case
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::146a9d3a3b29ac36a172ad4f75665f15
https://doi.org/10.1017/s0004972718000813
https://doi.org/10.1017/s0004972718000813
Publikováno v:
Monatshefte für Mathematik. 185:43-60
Given a normed plane $\mathcal{P}$, we call $\mathcal{P}$-cycloids the planar curves which are homothetic to their double $\mathcal{P}$-evolutes. It turns out that the radius of curvature and the support function of a $\mathcal{P}$-cycloid satisfy a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db2f165e98226e17bae6e33654737e97
https://doi.org/10.1007/s00605-017-1030-5
https://doi.org/10.1007/s00605-017-1030-5