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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
Published electronically: March 9, 2006
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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$.

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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