Transverse Hausdorff dimension of codim-1 C$^2$-foliations

Volume 149 / 1996

Takashi Inaba, Paweł Walczak Fundamenta Mathematicae 149 (1996), 239-244 DOI: 10.4064/fm-149-3-239-244

Abstract

The Hausdorff dimension of the holonomy pseudogroup of a codimension-one foliation ℱ is shown to coincide with the Hausdorff dimension of the space of compact leaves (traced on a complete transversal) when ℱ is non-minimal, and to be equal to zero when ℱ is minimal with non-trivial leaf holonomy.

Authors

  • Takashi Inaba
  • Paweł Walczak

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