Relative Kuo's condition and Thom's type inequality

Satoshi Koike (Hyogo)

Abstract

In a previous joint paper with Karim Bekka, we discussed the relationship between the Kuo condition and Thom's type inequality, and showed that they are equivalent. These conditions are equivalent to $$C^0$$-sufficiency of jets in the function case, and $$v$$-sufficiency of jets in the mapping case. They are local notions at a given point, e.g. $$0 \in \mathbb{R}^n$$. In this talk we discuss the relative notions to a given closed subset $$\Sigma$$ containing $$0 \in \mathbb{R}^n$$. This is also a joint work with K. Bekka.