On flat submaps of maps of nonpositive curvature

Autor:	Alexander Yu. Olshanskii, Mark Sapir
Rok vydání:	2018
Předmět:	Applied Mathematics General Mathematics 010102 general mathematics 0103 physical sciences Geometry 010307 mathematical physics 0101 mathematics Curvature 01 natural sciences Mathematics
Zdroj:	Transactions of the American Mathematical Society. 371:4869-4894
ISSN:	1088-6850 0002-9947
Popis:	We prove that for every r > 0 r>0 if a nonpositively curved ( p , q ) (p,q) -map M M contains no flat submaps of radius r r , then the area of M M does not exceed C r n Crn for some constant C C . This strengthens a theorem of Ivanov and Schupp. We show that an infinite ( p , q ) (p,q) -map which tessellates the plane is quasi-isometric to the Euclidean plane if and only if the map contains only finitely many nonflat vertices and faces. We also generalize Ivanov and Schupp’s result to a much larger class of maps, namely to maps with angle functions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::6f49e832e15338f73aa010ce4154f316 https://doi.org/10.1090/tran/7487 Zobrazit plný text záznamu