Inner Lipschitz approximation in o-minimal structures

Time: 9:30 - 11:00, 9 April 2026 (Thursday)

Venue: Room 507, A6, Institute of Mathematics

Online (Zoom meeting): https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Meeting ID: 996 3668 1387

Passcode: 123456

Abstract. In this talk, we show that,  in a given o-minimal structure, every definable mapping that is Lipschitz with respect to the inner metric can be approximated by $C^1$ mappings that are Lipschitz with respect to the inner metric with arbitrarily close bounds for the derivative. When the o-minimal structure admits $C^\infty$ cell decomposition, the approximating mapping can be chosen to be $C^\infty$. Furthermore, we extend this result to outer Lipschitz mappings. The proof relies on the construction of partitions of unity with sharp bounds for the derivative, which can be useful for other approximation problems. This is a joint work with G. Valette and A. Valette.