STABLE LOWER ESTIMATES FOR SMOOTH MAPPINGS AND FOR GRADIENTS OF SMOOTH FUNCTIONS
N N Nehorošev · Mathematics of the USSR-Sbornik · 1973
In this article is discussed a stable lower estimate for gradients of functions near a critical point. It is stable in the sense that if the function belongs to a family of functions depending smoothly on a finite-dimensional parameter, then the estimate will be correct for functions with close parameter values. Related to this estimate is a stratification of the space of jets of functions; the strata are semialgebraic sets of increasing codimension. Bibliography: 6 items.