KL-inequality for definable maps
Volume 128 / 2024
Banach Center Publications 128 (2024), 135-143
MSC: Primary 26D10; Secondary 03C64, 32B20
DOI: 10.4064/bc128-9
Abstract
We state and prove a version of the KL (Kurdyka-Łojasiewicz) inequality for a mapping definable in an o-minimal structure, with values in $\mathbb {R}^k$, $k \gt 1$. It implies a uniform bound for the measure of submanifolds transverse to the fibers.
