Stability of isometric maps in the Heisenberg group | Zendy

Nicola Arcozzi | Zendy; Daniele Morbidelli | Zendy

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Stability of isometric maps in the Heisenberg group

Author(s) -

Nicola Arcozzi,

Daniele Morbidelli

Publication year - 2008

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/120

Subject(s) - mathematics , heisenberg group , pointwise , mathematical analysis , ball (mathematics) , geodesic , norm (philosophy) , isometry (riemannian geometry) , group (periodic table) , pure mathematics , physics , quantum mechanics , political science , law

In this paper we prove some approximation results for biLipschitz maps in the Heisenberg group. Namely, we show that a biLipschitz map with biLipschitz constant close to one can be pointwise approximated, quantitatively on any xed ball, by an isometry. This leads to an approximation in BMO norm for the map’s Pansu derivative. We also prove that a global quasigeodesic can be approximated by a geodesic on any xed segment.

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