Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 339-356

REGULARITY OF THE DISTANCE FUNCTION TO SMOOTH HYPERSURFACES IN SOME TWO-STEP CARNOT GROUPS

Nicola Arcozzi, Fausto Ferrari and Francescopaolo Montefalcone

Università degli Studi di Bologna, Dipartimento di Matematica
Piazza di P.ta S.Donato, 5, 40126 Bologna, Italy; nicola.arcozzi 'at' unibo.it

Università degli Studi di Bologna, Dipartimento di Matematica
Piazza di P.ta S.Donato, 5, 40126 Bologna, Italy; fausto.ferrari 'at' unibo.it

Università di Padova, Dipartimento di Matematica Pura e Applicata
Via Trieste, 63, 35121 Padova, Italy; montefal 'at' math.unipd.it

Abstract. We study geometric properties of the Carnot–Carathéodory signed distance δ^s to a smooth hypersurface S in some 2-step Carnot groups. In particular, a sub-Riemannian version of Gauss' Lemma is proved.

2010 Mathematics Subject Classification: Primary 49Q15, 46E35, 22E60.

Key words: Carnot groups, sub-Riemannian geometry, CC-metrics, distance from hypersurfaces, metric normal, normal geodesics.

Reference to this article: N. Arcozzi, F. Ferrari and F. Montefalcone: Regularity of the distance function to smooth hypersurfaces in some two-step Carnot groups. Ann. Acad. Sci. Fenn. Math. 42 (2017), 339-356.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4222