Defesa de Tese: On Plane Minkowski Geometry

Aluno: Vitor Balestro Dias da Silva

Banca: Prof. Ralph Costa Teixeira (UFF - Orientador)

Prof. Daniele Sepe (UFF)

Prof. Marcos Craizer (PUC-Rio)

Prof. Moacyr Alvim Horta Barbosa da Silva (FGV-Rio)

Prof. Nilson da Costa Bernardes Junior (UFRJ)

Prof. Max Souza (UFF – suplente)

Co-Orientador: Prof. Horst Martini (TU Chemnitz) 

Data: 24 de agosto de 2016, 11h.

Local: Sala 407, Bloco H, IME, Campus Gragoatá, UFF.

Resumo: This thesis is devoted to provide a (threefold) contribution to the geometry of Minkowski planes (i.e., two-dimensional real vector spaces endowed with a norm). We introduce a new construction of Radon curves which only rely in Convex Geometry concepts, and also some new characterizations of such curves (in terms of collinearity and parallelism) are given. Geometric properties of trigonometric functions defined for Minkowski planes are investigated. Further, we define and study new geometric constants for normed planes. We use them to estimate how far a plane is from being Radon or Euclidean, and also to provide a quantitative difference between Birkhoff and Roberts orthogonality types. Extremal values are in most cases completely characterized.
Nota: a defesa será em Português.