Morse theory for min-type functions
In [\textit{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 [\textit{K. Grove}, Proc. Symp. Pure Math. 54, Part 3, 357-385 (1993; Zbl 0806.53043)] are given.
scientific article; zbMATH DE number 1186648