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A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2021-06-26 , DOI: 10.1007/s13398-021-01096-2 Álvaro Martínez-Pérez , José M. Rodríguez
中文翻译:
关于 Gromov 双曲流形和图的等周不等式的注记
更新日期:2021-06-28
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2021-06-26 , DOI: 10.1007/s13398-021-01096-2 Álvaro Martínez-Pérez , José M. Rodríguez
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.
中文翻译:
关于 Gromov 双曲流形和图的等周不等式的注记
我们在本文中研究了图和黎曼流形的等周不等式和双曲性的关系。我们根据 Gromov 边界获得了满足(Cheeger)等周不等式的图和黎曼流形(具有有界局部几何)的特征,改进了先前工作的类似结果。特别是,我们证明了有一个极点是等周不等式的必要条件,因此,它可以作为假设去除。