arXiv Open Access 2014

On the quantitative quasi-isometry problem: transport of Poincaré inequalities and different types of quasi-isometric distortion growth

Vladimir Shchur

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Abstrak

We consider a quantitative form of the quasi-isometry problem. We discuss several arguments which lead us to different results and bounds of quasi-isometric distortion: comparison of volumes, connectivity etc. Then we study the transport of Poincaré constants by quasi-isometries and we give sharp lower and upper bounds for the homotopy distortion growth for an interesting class of hyperbolic metric spaces.

Topik & Kata Kunci

math.MG

Penulis (1)

Vladimir Shchur

Format Sitasi

APA MLA BibTeX

Shchur, V. (2014). On the quantitative quasi-isometry problem: transport of Poincaré inequalities and different types of quasi-isometric distortion growth. https://arxiv.org/abs/1401.7315

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Informasi Jurnal

Tahun Terbit: 2014
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓