Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 1013–1063

INTRINSIC LIPSCHITZ GRAPHS IN CARNOT GROUPS OF STEP 2

Daniela Di Donato

Università di Trento, Dipartimento di Matematica
Via Sommarive 14, 38123, Povo (Trento), Italy; daniela.didonato 'at' unitn.it

Abstract. We provide a characterization of locally intrinsic Lipschitz functions in Carnot groups of step 2 in terms of their intrinsic distributional gradients. We also prove an area formula with respect to the spherical Hausdorff measure for the graph of an intrinsic Lipschitz function.

2010 Mathematics Subject Classification: Primary 35R03; Secondary 28A75, 53C17.

Key words: Carnot groups, intrinsic Lipschitz functions, intrinsic graphs, intrinsic regular hypersurfaces.

Reference to this article: D. Di Donato: Intrinsic Lipschitz graphs in Carnot groups of step 2. Ann. Acad. Sci. Fenn. Math. 45 (2020), 1013–1063.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4556