Whitney stratifications and the continuity of local Lipschitz Killing curvatures

TL;DR

This paper proves that local Lipschitz Killing curvatures are continuous along Whitney stratification strata for definable sets in polynomially bounded o-minimal structures, and are locally Lipschitz under (w)- regularity.

Contribution

It establishes the continuity and Lipschitz regularity of local Lipschitz Killing curvatures in a broad o-minimal setting, linking geometric stratification conditions to curvature behavior.

Findings

Continuity of local Lipschitz Killing curvatures along Whitney strata.

Lipschitz regularity of these curvatures under (w)- regular stratifications.

Applicability to definable sets in polynomially bounded o-minimal structures.

Abstract

We prove that local Lipschitz Killing curvatures of definable sets in a polynomially bounded o-minimal structure are continuous along strata of Whitney stratifications and locally Lipschitz if the stratifications are (w)- regular.