We consider submanifolds of sub-Riemannian Carnot groups with intrinsic C 1 regularity. Our first main result is an area formula for C 1 intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing C 1 submanifolds into level sets of a C 1 function.

Area of intrinsic graphs and coarea formula in Carnot groups

Julia, Antoine;Nicolussi Golo, Sebastiano
;
Vittone, Davide
2022

Abstract

We consider submanifolds of sub-Riemannian Carnot groups with intrinsic C 1 regularity. Our first main result is an area formula for C 1 intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing C 1 submanifolds into level sets of a C 1 function.
File in questo prodotto:
File Dimensione Formato  
22-Julia_NicolussiGolo_V-MathZ.pdf

accesso aperto

Descrizione: JNGV-MathZ
Tipologia: Published (publisher's version)
Licenza: Creative commons
Dimensione 631.01 kB
Formato Adobe PDF
631.01 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3412143
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 6
social impact