20 citations · 147 across the 16 of their papers we have counts for
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math.FA2012★ 17 cited
Geometric Sobolev-like embedding using high-dimensional Menger-like curvature
Sławomir Kolasiński
We study a modified version of Lerman-Whitehouse Menger-like curvature defined for m+2 points in an n-dimensional Euclidean space. For 1 <= l <= m+2 and an m-dimensional subset S o…
math.FA2011★ 7 cited
Minimal Hölder regularity implying finiteness of integral Menger curvature
Sławomir Kolasiński, Marta Szumańska
We study two families of integral functionals indexed by a real number . One family is defined for 1-dimensional curves in and the other one is defined for -dimens…
math.FA2011★ 17 cited
Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds
Simon Blatt, Sławomir Kolasiński
In this paper we show that embedded and compact manifolds have finite integral Menger curvature if and only if they are locally graphs of certain Sobolev-Slobodeckij spaces.…