Locally geodesically quasiconvex functions on complete Riemannian manifolds

Yamaguchi, Takao

doi:10.1090/S0002-9947-1986-0857446-4

Locally geodesically quasiconvex functions on complete Riemannian manifolds
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Trans. Amer. Math. Soc. 298 (1986), 307-330 Request permission

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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