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A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs

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URI: https://hdl.handle.net/10016/35497
ISSN: 1579-1505
DOI: https://doi.org/10.1007/s13398-021-01096-2
UXXI: AR/0000030821
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isoperimetric_RACSAM_2021.pdf (226.93 KB)
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2021-06-26
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Springer Science and Business Media LLC
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Abstract
We study in this paper the relationship of isoperimetric inequality and hyperbolicity for graphs and Riemannian manifolds. We obtain a characterization of graphs and Riemannian manifolds (with bounded local geometry) satisfying the (Cheeger) isoperimetric inequality, in terms of their Gromov boundary, improving similar results from a previous work. In particular, we prove that having a pole is a necessary condition to have isoperimetric inequality and, therefore, it can be removed as hypothesis.
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Cheeger Isoperimetric Constant, Gromov Hyperbolicity, Bounded Local Geometry, Pole
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Martínez-Pérez, Á., & Rodríguez, J. M. (2021). A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs. In Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (Vol. 115, Issue 3). Springer Science and Business Media LLC.
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