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arXiv:1312.1675 [math.GT]AbstractReferencesReviewsResources

Components of spaces of curves with constrained curvature on flat surfaces

Nicolau C. Saldanha, Pedro Zühlke

Published 2013-12-05, updated 2014-11-03Version 4

Let $S$ 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 $S$ 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.

Comments: 38 pages, 11 figures. In this version, some results in section 7 which were not used elsewhere were removed to make the paper shorter and less technical. Also, the notation in section 3 has been changed slightly to make it compatible with arXiv:1410.8590
Categories: math.GT, math.DG
Subjects: 53A04, 53C42, 57N20
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