Spaces of curves with constrained curvature on flat surfaces, I
Nicolau C. Saldanha, Pedro Zühlke · arXiv (Cornell University) · 2013
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.