Mathematische Zeitschrift

, Volume 256, Issue 3, pp 661–684

Metric normal and distance function in the Heisenberg group


DOI: 10.1007/s00209-006-0098-8

Cite this article as:
Arcozzi, N. & Ferrari, F. Math. Z. (2007) 256: 661. doi:10.1007/s00209-006-0098-8


We introduce a notion which is equivalent in the Heisenberg group \(\mathbb{H}\) to that of segment normal to a surface. Then, we study some regularity properties of the function measuring the Carnot-Carathéodory distance from an Euclidean surface S in \(\mathbb{H}\) in terms of the regularity of S.

Mathematics Subject Classification (2000)

49Q15 53C17 53C22 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Dipartimento di Matematicadell’Università di BolognaBolognaItaly
  2. 2.C.I.R.A.MBolognaItaly

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