We propose a notion of integral Menger curvature for compact, $m$-dimensionalsets in $n$-dimensional Euclidean space and prove that finiteness of thisquantity implies that the set is $C^{1,\alpha}$ embedded manifold with theH{\"o}lder norm and the size of maps depending only on the curvature. Wedevelop the ideas introduced by Strzelecki and von der Mosel [Adv. Math.226(2011)] and use a similar strategy to prove our results.
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机译：我们为$ n $维欧氏空间中的紧致$ m $维集提出了积分Menger曲率的概念，并证明了这种数量的有限性意味着该集是$ C ^ {1，\ alpha} $嵌入有H { \“ o} der范数和地图的大小仅取决于曲率。我们开发了Strzelecki和von der Mosel [Adv。Math.226（2011）]引入的思想，并使用类似的策略来证明我们的结果。
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