Findings demonstrate the equivalence and preservation of inequalities in Riemannian manifolds under quasi-isometries.
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.
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Granados et al. (2026) studied this question.
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