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Components of spaces
of curves with constrained curvature on flat surfaces
Nicolau C. Saldanha and Pedro Zühlke |
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Vol. 281 (2016), No. 1, 185–242
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Abstract |
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Let be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval, in terms of all parameters involved. Many topological properties of these spaces are investigated. Some conjectures of L. E. Dubins are proved. |
Keywords
curve, curvature, Dubins path, flat surface, topology of
infinite-dimensional manifolds
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Mathematical Subject Classification 2010
Primary: 53A04
Secondary: 53C42, 57N20
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Milestones
Received: 5 November 2014
Revised: 16 July 2015
Accepted: 19 July 2015
Published: 9 February 2016
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Authors |
| Nicolau C. Saldanha | |
| Departamento de Matemática Pontifícia Universidade Católica do Rio de Janeiro Rua Marquês de Sao Vicente 225 Rio de Janeiro, RJ 22453-900 Brazil |
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| Pedro Zühlke | |
| Instituto de Matemática e
Estatística Universidade de São Paulo Rua do Matão 1010 IME - Cidade Universitária São Paulo, SP 05508-090 Brazil |
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