Averaging submanifolds of riemannian manifolds
How can one define the "average" of two or more nearby
(unparametrized) space curves in a way which is invariant under interchange
of the curves? This innocent-looking question turns out to be suprisingly
difficult. I will describe several approaches which have not (yet)
worked and one which has. More generally, I will present an averaging
theorem for submanifolds of riemannian manifolds, and an application to
finding invariant manifolds for actions of compact groups.
The talk is based on a paper
to appear in the new Journal
of the European Mathematical Society (and posted at the xxx
archive).
Winter
2000 meeting of the PNGS