Geodesic
Almost invariant submanifolds for compact group actions
Journal of the European Mathematical Society, Tome 2 (2000) no. 1, pp. 53-86.

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Abstract. We define a C1 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 C1-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.
DOI : 10.1007/s100970050014
Classification : 53-XX, 57-XX, 00-XX
Keywords: 
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     author = {Alan Weinstein},
     title = {Almost invariant submanifolds for compact group actions},
     journal = {Journal of the European Mathematical Society},
     pages = {53--86},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2000},
     doi = {10.1007/s100970050014},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970050014/}
}
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Alan Weinstein. Almost invariant submanifolds for compact group actions. Journal of the European Mathematical Society, Tome 2 (2000) no. 1, pp. 53-86. doi : 10.1007/s100970050014. http://geodesic.mathdoc.fr/articles/10.1007/s100970050014/

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