arXiv Open Access 2017

On flat submaps of maps of non-positive curvature

A. Yu. Olshanskii M. V. Sapir

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Abstrak

We prove that for every $r>0$ if a non-positively curved $(p,q)$-map $M$ contains no flat submaps of radius $r$, then the area of $M$ does not exceed $Crn$ for some constant $C$. This strengthens a theorem of Ivanov and Schupp. We show that an infinite $(p,q)$-map which tessellates the plane is quasi-isometric to the Euclidean plane if and only if the map contains only finitely many non-flat vertices and faces. We also generalize Ivanov and Schupp's result to a much larger class of maps, namely to maps with angle functions.

Topik & Kata Kunci

math.GR

Penulis (2)

A. Yu. Olshanskii

M. V. Sapir

Format Sitasi

APA MLA BibTeX

Olshanskii, A.Y., Sapir, M.V. (2017). On flat submaps of maps of non-positive curvature. https://arxiv.org/abs/1702.08205

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Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓