Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds

Details Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds

2011-10-21

arxiv.org/abs/1110.4786v1

Mathematics

Functional Analysis

Scientific paper

In this paper we show that embedded and compact $C^1$ manifolds have finite
integral Menger curvature if and only if they are locally graphs of certain
Sobolev-Slobodeckij spaces. Furthermore, we prove that for some intermediate
energies of integral Menger type a similar characterization of objects with
finite energy can be given.

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