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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On complete graphs with negative r-mean curvature


Author: Maria Fernanda Elbert
Journal: Proc. Amer. Math. Soc. 128 (2000), 1443-1450
MSC (2000): Primary 53C42; Secondary 53A10
Published electronically: February 7, 2000
MathSciNet review: 1712913
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Abstract: We generalize Efimov's Theorem for graphs in Euclidean space using the scalar curvature, with an additional hypothesis on the second fundamental form.


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Additional Information

Maria Fernanda Elbert
Affiliation: Instituto de Matematica, UFRJ, Cx. Postal 68530, 21941-590 Rio de Janeiro, RJ, Brasil
Address at time of publication: IMPA - Estrada Dona Castorina, 110, 22460-320 - Rio de Janeiro, RJ, Brasil
Email: elbert@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05671-9
PII: S 0002-9939(00)05671-9
Keywords: Negative r-mean curvature, complete graphs, divergence, Cheeger constant
Received by editor(s): June 17, 1998
Published electronically: February 7, 2000
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society