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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Locally geodesically quasiconvex functions on complete Riemannian manifolds


Author: Takao Yamaguchi
Journal: Trans. Amer. Math. Soc. 298 (1986), 307-330
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9947-1986-0857446-4
MathSciNet review: 857446
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Abstract: In this article, we investigate the topological structure of complete Riemannian manifolds admitting locally geodesically quasiconvex functions, whose family includes all geodesically convex functions. The existence of a locally geodesically quasiconvex function is equivalent to the existence of a certain filtration by locally convex sets. Our argument contains Morse theory for the lower limit function of a given locally geodesically quasiconvex function.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0857446-4
Article copyright: © Copyright 1986 American Mathematical Society