Noncircular algebraic curves of constant width: an answer to Rabinowitz

Autor: Yves Martinez-Maure

Publikováno v: Canadian Mathematical Bulletin. 65:552-556

In response to an open problem raised by S. Rabinowitz, we prove that $$ \begin{align*} \begin{array} [c]{l} \left( \left( x^{2}+y^{2}\right) {}^{2}+8y\left( y^{2}-3x^{2}\right) \right) {}^{2}+432y\left( y^{2}-3x^{2}\right) \left( 351-10\left( x^{2}+

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c46864c7c0a20112384c9df3adc8e89a
https://doi.org/10.4153/s0008439521000473

Real and complex hedgehogs, their symplectic area, curvature and evolutes

Autor: Yves Martinez-Maure

Classical (real) hedgehogs can be regarded as the geometrical realiza-tions of formal di¤erences of convex bodies in R n+1. Like convex bodies, hedgehogs can be identi…ed with their support functions. Adopting a pro-jective viewpoint, we prove tha

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e21fe573a9554ea5487e5fdcf3762772
https://hal.archives-ouvertes.fr/hal-02948386/document

Existence and uniqueness theorem for a 3-dimensional polytope in R3 with prescribed directions and perimeters of the facets

Autor: Yves Martinez-Maure

Publikováno v: Discrete Mathematics. 343:111770

We give a set of conditions that is necessary and sufficient for the existence and uniqueness up to translations of a 3-dimensional polytope P in R 3 having N facets with given unit outward normal vectors n 1 , … , n N and corresponding facet perim

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e3a9622cfa3b7926a97a61420947ee1d
https://doi.org/10.1016/j.disc.2019.111770

Tout chemin générique de hérissons réalisant un retournement de la sphère dans $\mathbb{R}^3$ comprend un hérisson porteur de queues d’aronde positives

Autor: Yves Martinez-Maure

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publ. Mat. 59, no. 2 (2015), 339-351
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)

Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski differences of convex bodies in $\mathbb{R}^{n+1}$. They are the natural geometrical objects when one seeks to extend parts of the Brunn-Minkowski theory to

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bff419788f713d7db2f8e2f97894bfec
https://doi.org/10.5565/publmat_59215_04

Dérivation des surfaces convexes de dans l'espace de Lorentz et étude de leurs focales

Autor: Yves Martinez-Maure

Publikováno v: Comptes Rendus Mathematique. 348:1307-1310

Resume En introduisant une notion de derivation des surfaces convexes de R 3 dans l'espace de Lorentz–Minkowski R 3 , 1 , nous donnons pour les surfaces convexes de R 3 un equivalent naturel d'une majoration du deficit isoperimetrique des courbes c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::cc1ccb6ae5696e16e43dd32316c9b9a5
https://doi.org/10.1016/j.crma.2010.10.029