Dick Palais
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 Nov 18 awarded Good Answer Nov 2 awarded Popular Question Sep 30 comment About Palais' remark that an isometry of Riemannian manifolds does not induce an isometry of the Hilbert manifolds of curves The problem lies in the line above defining $g_\sigma(λ,μ)$. This is the metric for $H_0$, NOT the metric for $H_1$. The correct definition of the metric for $H_1$ uses $⟨λ'(t),μ'(t)⟩$ rather than $⟨λ(t),μ(t)⟩$ (see page 222 of my article where both metrics are defined), and with this change it is fairly obvious why my remark in the cited paper is in fact correct. Aug 23 comment Algorithm for finding inverse images of a local diffeomorphism Yes! Newton's Method is clearly the way to go. For $k=1$, the algorithm I wrote in fact did use Newton's Method, (rather than bisection) since it is much faster. But I guess I forgot that Newton's Method works in higher dimensions too. Thanks Ryan. Aug 23 accepted Algorithm for finding inverse images of a local diffeomorphism Aug 22 comment Algorithm for finding inverse images of a local diffeomorphism @Nanda For the application I have in mind, F will be given by a formula. Aug 22 asked Algorithm for finding inverse images of a local diffeomorphism Aug 4 awarded Popular Question Aug 3 awarded Good Answer Jul 11 comment What is a good method to find random points on the n-sphere when n is large? @Mark Meckes Many thanks, Mark. In retrospect, if I had been more adept with my Googling I might have discovered that the Gaussian RV approach was a "well-known" answer to my question, and would not have needed to ask it on MO. But as usual, I have come away very impressed with the utility of this great website and learned a lot from the answers I received. Jul 11 accepted What is a good method to find random points on the n-sphere when n is large? Jul 11 awarded Nice Question Jul 10 asked What is a good method to find random points on the n-sphere when n is large? Jul 4 awarded Yearling Jun 25 awarded Generalist Jun 25 awarded dg.differential-geometry Jun 25 awarded Revival Jun 25 awarded Pundit Jun 14 answered Calculus book in the spirit of the 18th century Jun 9 answered Mathematics for ebook readers