Riemannian manifolds with curvature at most $\kappa$: Gluing with ramification
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N. N. Kosovskiĭ
Translated by: the author - St. Petersburg Math. J. 16 (2005), 703-711
- DOI: https://doi.org/10.1090/S1061-0022-05-00874-5
- Published electronically: June 23, 2005
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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
- Stephanie B. Alexander, I. David Berg, and Richard L. Bishop, Geometric curvature bounds in Riemannian manifolds with boundary, Trans. Amer. Math. Soc. 339 (1993), no. 2, 703–716. MR 1113693, DOI 10.1090/S0002-9947-1993-1113693-1
- N. N. Kosovskiĭ, Gluing of Riemannian manifolds of curvature $\geq \kappa$, Algebra i Analiz 14 (2002), no. 3, 140–157 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 14 (2003), no. 3, 467–478. MR 1921991
- N. N. Kosovskiĭ, Gluing of Riemannian manifolds of curvature $\leq \kappa$, Algebra i Analiz 14 (2002), no. 5, 73–86 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 14 (2003), no. 5, 765–773. MR 1970333
- Yu. G. Rešetnyak, On the theory of spaces with curvature no greater than $K$, Mat. Sb. (N.S.) 52 (94) (1960), 789–798 (Russian). MR 0121762
Bibliographic Information
- N. N. Kosovskiĭ
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Email: kosovnn@pdmi.ras.ru
- Received by editor(s): October 6, 2003
- Published electronically: 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 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 703-711
- MSC (2000): Primary 53C21, 53C22
- DOI: https://doi.org/10.1090/S1061-0022-05-00874-5
- MathSciNet review: 2090854