In mathematics, the Menger curvature of a triple of points in n-dimensional Euclidean space R n is the reciprocal of the radius of the circle that passes through the three points. It is named after …

Menger curvature and rectifiability By J. C. LEGER Introduction Let us first introduce some basic definitions needed to better understand this introduction and the rest of the paper. For a Borel …

2008年12月20日 · We show that for any metric space X the condition ∫ X ∫ X ∫ X c (z 1, z 2, z 3) 2 d H 1 z 1 d H 1 z 2 d H 1 z 3 < ∞, where c (z 1, z 2, z 3) is the Menger curvature of the triple (z …

In this paper, we wish to explore how Menger-type curvatures, see Definitions 2.6 and 2.8, yield information about C1 ,α n-rectifiability, see Definition 2.3, of measures. In 1995, Melnikov …

Menger曲率则巧妙地将几何测度论、奇异积分算子和有界解析函数的可去奇点问题联系起来。.我们将研究任意维空间的Menger曲率问题，并用其刻划一些分形集合的光滑性和奇异积分算子 …

1999年5月1日 · Abstract: For a Borel set E in R^n, the total Menger curvature of E, or c(E), is the integral over E^3 (with respect to 1-dimensional Hausdorff measure in each factor of E) of …

2019年12月12日 · In this paper, we wish to explore how Menger-type curvatures, see Definitions 2.6 and 2.8, yield information about \(C^{1,\alpha }\) n-rectifiability, see Definition 2.3, of …

2019年8月29日 · Abstract page for arXiv paper 1908.11471: Menger curvatures and $C^{1,α}$ rectifiability of measures We further develop the relationship between $β$-numbers and …

2004年10月20日 · In: Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral. Lecture Notes in Mathematics, vol 1799. Springer, Berlin, Heidelberg. …

In mathematics, the curvature of a measure defined on the Euclidean plane R 2 is a quantification of how much the measure's "distribution of mass" is "curved". It is related to notions of …