A Gromov’s dimension comparison estimate for rectifiable sets

• Valentino Magnani ^[1] ; Aleksandra Zapadinskaya ^[1]
  1. [1] Dipartimento di Matematica
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1153-1174
• Idioma: inglés
• DOI: 10.1007/s00029-017-0304-z
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• Resumen

  • We extend the validity of a Gromov’s dimension comparison estimate for topological hypersurfaces to sufficiently large classes of rectifiable sets, arising from Sobolev mappings. Our tools are a suitably weak exterior differentiation for pullback differential forms and a new low rank property for Sobolev mappings