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- W2964004227 abstract "We prove isotopy finiteness for various geometric curvature energies including integral Menger curvature, and tangent-point repulsive potentials, defined on the class of compact, embedded m-dimensional Lipschitz submanifolds in R n . That is, there are only finitely many isotopy types of such submanifolds below a given energy value, and we provide explicit bounds on the number of isotopy types in terms of the respective energy. Moreover, we establish C 1 -compactness: any sequence of submanifolds with uniformly bounded en- ergy contains a subsequence converging inC 1 to a limit submanifold with the same energy bound. In addition, we show that all geometric curvature energies under consideration are lower semicontinuous with respect to Hausdor-converge nce, which can be used to min- imise each of these energies within prescribed isotopy classes." @default.
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- W2964004227 date "2018-01-01" @default.
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- W2964004227 title "Compactness and isotopy finiteness for submanifolds with uniformly bounded geometric curvature energies" @default.
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- W2964004227 doi "https://doi.org/10.4310/cag.2018.v26.n6.a2" @default.
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