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<p>Quasi-isometries are a versatile type of maps that preserve the large-scale geometry of spaces, while introducing significant local distortions. Following Kanai’s work, which established the invariance of various analytic and geometric properties under quasi-isometries, this paper generalizes isoperimetric and Sobolev inequalities for exponents less than the manifold’s dimension, proving both that they are equivalent and preserved by quasi-isometries.</p>

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Stability of isoperimetric and Sobolev inequalities for excluded exponents on Riemannian manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月20日

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  • Ana Granados,
  • Ana Portilla,
  • José M. Rodríguez,
  • Eva Tourís

摘要

Quasi-isometries are a versatile type of maps that preserve the large-scale geometry of spaces, while introducing significant local distortions. Following Kanai’s work, which established the invariance of various analytic and geometric properties under quasi-isometries, this paper generalizes isoperimetric and Sobolev inequalities for exponents less than the manifold’s dimension, proving both that they are equivalent and preserved by quasi-isometries.