The isoperimetric inequality on sub-Riemannian manifolds of conformally-hyperbolic type (Q2759271)
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scientific article; zbMATH DE number 1681676
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The isoperimetric inequality on sub-Riemannian manifolds of conformally-hyperbolic type |
scientific article; zbMATH DE number 1681676 |
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The isoperimetric inequality on sub-Riemannian manifolds of conformally-hyperbolic type (English)
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13 May 2003
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sub-Riemannian manifold
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isoperimetric inequality
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An isoperimetric inequality is a relation of the form \(P(V(D)) < S(Fr D)\) between the volume \(V(D)\) of a domain \(D\) and the area \(S(Fr D)\) of its boundary, where \(P\) is a function called the isoperimetric function of the space. A manifold \(M\) endowed with a subbundle \(H\) of the tangent bundle \(TM\) and a Riemannian structure \(g\) on \(H\) is called a sub-Riemannian manifold. The authors' basic results of [Usp. Mat. Nauk 54, 665-666 (1999; Zbl 0977.53032)] on the canonical form of the isoperimetric inequality on Riemannian manifolds of conformally-hyperbolic type are extended here to sub-Riemannian manifolds.
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