Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group

Bernd Kirchheim[1]; Francesco Serra Cassano[2]

  • [1] Dipartimento di Matematica Mathematical Institute University of Oxford 24-29 St Giles’ Oxford, OX1 3LB, UK
  • [2] Dipartimento di Matematica Università di Trento Via Sommarive, 14 38050 Povo (Trento), Italia

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 4, page 871-896
  • ISSN: 0391-173X

Abstract

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We construct an intrinsic regular surface in the first Heisenberg group 1 3 equipped wiht its Carnot-Carathéodory metric which has euclidean Hausdorff dimension  2 . 5 . Moreover we prove that each intrinsic regular surface in this setting is a 2 -dimensional topological manifold admitting a 1 2 -Hölder continuous parameterization.

How to cite

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Kirchheim, Bernd, and Serra Cassano, Francesco. "Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.4 (2004): 871-896. <http://eudml.org/doc/84551>.

@article{Kirchheim2004,
abstract = {We construct an intrinsic regular surface in the first Heisenberg group $\mathbb \{H\}^\{1\} \equiv \mathbb \{R\}^\{3\}$ equipped wiht its Carnot-Carathéodory metric which has euclidean Hausdorff dimension $2.5$. Moreover we prove that each intrinsic regular surface in this setting is a $2$-dimensional topological manifold admitting a $\frac\{1\}\{2\}$-Hölder continuous parameterization.},
affiliation = {Dipartimento di Matematica Mathematical Institute University of Oxford 24-29 St Giles’ Oxford, OX1 3LB, UK; Dipartimento di Matematica Università di Trento Via Sommarive, 14 38050 Povo (Trento), Italia},
author = {Kirchheim, Bernd, Serra Cassano, Francesco},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {871-896},
publisher = {Scuola Normale Superiore, Pisa},
title = {Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group},
url = {http://eudml.org/doc/84551},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Kirchheim, Bernd
AU - Serra Cassano, Francesco
TI - Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 4
SP - 871
EP - 896
AB - We construct an intrinsic regular surface in the first Heisenberg group $\mathbb {H}^{1} \equiv \mathbb {R}^{3}$ equipped wiht its Carnot-Carathéodory metric which has euclidean Hausdorff dimension $2.5$. Moreover we prove that each intrinsic regular surface in this setting is a $2$-dimensional topological manifold admitting a $\frac{1}{2}$-Hölder continuous parameterization.
LA - eng
UR - http://eudml.org/doc/84551
ER -

References

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