Spread: A Measure of the Size of Metric Spaces

Motivated by Leinster-Cobbold measures of biodiversity, the notion of the spread of a finite metric space is introduced. This is related to Leinster’s magnitude of a metric space. Spread is generalized to infinite metric spaces equipped with a measure and is calculated for spheres and straight lines. For Riemannian manifolds the spread is related to the volume and total scalar curvature. A notion of scale-dependent dimension is introduced and seen for approximations to certain fractals to be numerically close to the Minkowski dimension of the original fractals.

• Publication year

  2012

• Venue

  International journal of computational geometry and applications

• Publication date

  2012-09-11

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1142/S0218195915500120arXiv 1209.2300
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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