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St. Petersburg Mathematical Journal
ISSN 1547-7371(e) ISSN 1061-0022(p)

     
     

Riemannian manifolds with curvature at most $\kappa$: Gluing with ramification

Author(s): N. N. Kosovskii
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), vypusk 4.
Journal: St. Petersburg Math. J. 16 (2005), 703-711.
MSC (2000): Primary 53C21, 53C22
Posted: June 23, 2005
MathSciNet review: 2090854
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Abstract | References | Similar articles | Additional information

Abstract: Under some necessary conditions, the result of attaching several Riemannian manifolds along some isometry of their boundaries has curvature at most $\kappa$ in Aleksandrov's sense.

References:

[ABB]
S. B. Alexander, I. D. Berg, and R. L. Bishop, Geometric curvature bounds in Riemannian manifolds with boundary, Trans. Amer. Math. Soc. 339 (1993), no. 2, 703-716. MR 1113693 (93m:53034)

[K1]
N. N. Kosovskii, Gluing Riemannian manifolds of curvature at least $\kappa$, Algebra i Analiz 14 (2002), no. 3, 140-157; English transl., St. Petersburg Math. J. 14 (2003), no. 3, 467-478. MR 1921991 (2003d:53053)

[K2]
-, Gluing Riemannian manifolds of curvature at most $\kappa$, Algebra i Analiz 14 (2002), no. 5, 73-86; English transl., St. Petersburg Math. J. 14 (2003), no. 5, 765-774. MR 1970333 (2004g:53044)

[R]
Yu. G. Reshetnyak, On the theory of spaces with curvature no greater than $K$, Mat. Sb. (N.S.) 52 (1960), 789-798. (Russian) MR 0121762 (22:12496)

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Additional Information:

N. N. Kosovskii
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: kosovnn@pdmi.ras.ru

DOI: 10.1090/S1061-0022-05-00874-5
PII: S 1061-0022(05)00874-5
Keywords: Aleksandrov spaces, curvature, Riemannian manifold, polyhedral space
Received by editor(s): 6/OCT/2003
Posted: June 23, 2005
Additional Notes: Supported by CRDF (grant no. RM1-281-ST-02) and by RFBR (grant nos. 02-01-00090 and NSh--1914.2003.1)
Copyright of article: Copyright 2005, American Mathematical Society




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