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Morse theory for min-type functions. (English) Zbl 0921.58006

In [M. Gromov, Comment. Math. Helv. 56, 179-195 (1981; Zbl 0467.53021)] it is shown that the Morse theory for Riemannian distance functions can be developed by analogy with the classical Morse theory.
The aim of this article is to construct a Morse theory for functions which are minima of finite families of smooth functions and clarify the connection with Riemannian distance functions for non-positively curved manifolds. Relations with the Grove-Shiohama-Gromov approach [K. Grove, Proc. Symp. Pure Math. 54, Part 3, 357-385 (1993; Zbl 0806.53043)] are given.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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