Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

On graph approximations of surfaces with small area


Author: N. Zinov'ev
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), nomer 3.
Journal: St. Petersburg Math. J. 17 (2006), 435-442
MSC (2000): Primary 53C23
DOI: https://doi.org/10.1090/S1061-0022-06-00912-5
Published electronically: March 9, 2006
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that, for every closed oriented surface $ M$ of genus $ g$ with an arbitrary Riemann metric, there exists a metric graph of genus at most $ g$ such that the Gromov-Hausdorff distance between $ M$ and $ \Gamma$ does not exceed $ C\sqrt{{\mathrm{Vol}}M}$, where $ C$ depends only on $ g$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 53C23

Retrieve articles in all journals with MSC (2000): 53C23


Additional Information

DOI: https://doi.org/10.1090/S1061-0022-06-00912-5
Keywords: Closed oriented two-dimensional manifold, genus, Gromov--Hausdorff distance, metric graph
Received by editor(s): July 5, 2004
Published electronically: March 9, 2006
Additional Notes: Partially supported by NSF (grant DMS-0412166) and by NS (grant no. 1914.2003.1)
Article copyright: © Copyright 2006 American Mathematical Society

American Mathematical Society