| 概要 | Let X be a closed manifolds and f: X \times X --> R be a smooth function. Define f_n: X^{n+1} --> R by f_n(x_0,...,x_n) = 1/n \sigma f(x_i, x_{i+1}). We study the asymptotic distribution of the critical values of f_n as n goes to infinity. The main result says that "Critical values of f_n distribute densely in some interval as n goes to infinity." This is joint work with Masaki Tsukamoto (Kyoto university).
|