Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms
| Title: | Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms |
| Author: |
Michor, Peter W.; Mumford, David Bryant
Note: Order does not necessarily reflect citation order of authors. |
| Citation: | Michor, Peter W., and David Bryant Mumford. 2005. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Documenta Mathematica 10: 217-245. |
| Full Text & Related Files: |
Mumford_VanishingGeodDist.pdf (245.4Kb; PDF) 
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| Abstract: | The L^2-metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type M in a Riemannian manifold (N, g) induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance is a good topological metric. The vanishing phenomenon for the geodesic distance holds also for all diffeomorphism groups for the L^2-metric. |
| Published Version: | http://www.math.uiuc.edu/documenta/ |
| Other Sources: | http://www.dam.brown.edu/people/mumford/Papers/DigitizedVisionPapers--forNonCommercialUse/x05b--Vanishing-Michor.pdf |
| Terms of Use: | This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637112 |
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