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math.DG2012★ 5 cited
The space of non-degenerate closed curves in a Riemannian manifold
Jacob Mostovoy, Rustam Sadykov
Let LM be the semigroup of non-degenerate based loops with a fixed initial/final frame in a Riemannian manifold M of dimension at least three. We compare the topology of LM to that…
math.DG2012
Approximations of periodic functions to R^n by curvatures of closed curves
Jacob Mostovoy, Rustam Sadykov
We show that for any n real periodic functions f_1,..., f_n with the same period, such that f_i>0 for i<n, and a real number e >0, there is a closed curve in R^{n+1} with curvature…