Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds
Abstract
In this paper we show that embedded and compact C1 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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