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Limitations on the smooth confinement of an unstretchable manifold
We prove that an m-dimensional unit ball Dm in the Euclidean space Rm cannot be isometrically embedded into a higher-dimensional Euclidean ball BrdāRd of radius r<1/2 unless one of two conditions is met: (1) the embedding manifold has dimension dā©¾2m; (2) the embedding is not smooth. The proof uses differential ā¦