6533b81ffe1ef96bd12770ec
RESEARCH PRODUCT
Menger curvature and rectifiability in metric spaces
Immo Hahlomaasubject
Mathematics(all)Pure mathematicsGeneral MathematicsMathematical analysisMetric Geometry (math.MG)Metric spaceMenger curvatureHausdorff distanceMathematics - Metric GeometryMenger curvatureFOS: MathematicsHausdorff measureRectifiability28A75Metric spaceMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-12-01 |