Search results for "Menger curvature"

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Menger curvature and rectifiability in metric spaces

2008

We show that for any metric space $X$ the condition \[ \int_X\int_X\int_X c(z_1,z_2,z_3)^2\, d\Hm z_1\, d\Hm z_2\, d\Hm z_3 < \infty, \] where $c(z_1,z_2,z_3)$ is the Menger curvature of the triple $(z_1,z_2,z_3)$, guarantees that $X$ is rectifiable.

Mathematics(all)Pure mathematicsGeneral MathematicsMathematical analysisMetric Geometry (math.MG)Metric spaceMenger curvatureHausdorff distanceMathematics - Metric GeometryMenger curvatureFOS: MathematicsHausdorff measureRectifiability28A75Metric spaceMathematics
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Menger curvature and $C^{1}$ regularity of fractals

2000

Pure mathematicsFractalApplied MathematicsGeneral MathematicsMenger curvatureTopologyMathematicsProceedings of the American Mathematical Society
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Menger curvature and Lipschitz parametrizations in metric spaces

2005

Uniform continuityAlgebra and Number TheoryInjective metric spaceMathematical analysisMenger curvatureMetric mapLipschitz continuityMetric differentialMathematicsConvex metric spaceIntrinsic metricFundamenta Mathematicae
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