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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Accessible domains in the Heisenberg group


Authors: Zoltán M. Balogh and Roberto Monti
Journal: Proc. Amer. Math. Soc. 132 (2004), 97-106
MSC (2000): Primary 43A80, 22E30
Published electronically: March 25, 2003
MathSciNet review: 2021252
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Abstract: We study the problem of accessibility of boundary points for domains in the sub-Riemannian setting of the first Heisenberg group. A sufficient condition for accessibility is given. It is a Dini-type continuity condition for the horizontal gradient of the defining function. The sharpness of this condition is shown by examples.


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Additional Information

Zoltán M. Balogh
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland
Email: zoltan.balogh@math-stat.unibe.ch

Roberto Monti
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland
Email: roberto.monti@math-stat.unibe.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06978-8
PII: S 0002-9939(03)06978-8
Keywords: Heisenberg group, boundary accessibility, Dini continuity
Received by editor(s): August 8, 2002
Published electronically: March 25, 2003
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2003 American Mathematical Society