Blow-up of regular submanifolds in Heisenberg groups and applications

• Autorzy: Valentino Magnani
• Języki publikacji: EN

Abstrakty

EN

We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence of currents. Another application is the proof of an intrinsic coarea formula for vector-valued mappings on the Heisenberg group.

Słowa kluczowe

EN

Heisenberg group; submanifolds; Hausdorff measure; coarea formula; 28A75; 22E25

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 1
• Strony: 82-109

Daty

wydano

2006-03-01

online

2006-03-01

Twórcy

autor

Valentino Magnani

• Pisa University

Bibliografia

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Identyfikatory

DOI

10.1007/s11533-005-0006-1