Abstract.
We define a C 1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C 1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections of extended normal bundles.
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Received September 14, 1999 / final version received November 29, 1999
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Weinstein, A. Almost invariant submanifolds for compact group actions. J. Eur. Math. Soc. 2, 53–86 (2000). https://doi.org/10.1007/s100970050014
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DOI: https://doi.org/10.1007/s100970050014