23 Feb
2007
23 Feb
'07
9:46 a.m.
On 2/22/07, Fred lunnon <fred.lunnon@gmail.com> wrote:
It's not at all clear to me at this stage whether such an embedding, and hence the resulting curve, would necessarily be unique --- indeed, I strongly suspect it may not be.
On reflection, the curve is obviously not unique! Any (diffeo-)automorphism of the circle could precede a chosen embedding, generating in general a distinct curve from the same "curvature function". All this complication is a result of the multiple connectivity of the closed curve: the end-points and their differentials have somehow to be "joined up". WFL