Skip to main content
Log in

Polar coordinates in Carnot groups

  • Original article
  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

Abstract.

We describe a procedure for constructing ”polar coordinates” in a certain class of Carnot groups. We show that our construction can be carried out in groups of Heisenberg type and we give explicit formulas for the polar coordinate decomposition in that setting. The construction makes use of nonlinear potential theory, specifically, fundamental solutions for the p-sub-Laplace operators. As applications of this result we obtain exact capacity estimates, representation formulas and an explicit sharp constant for the Moser-Trudinger inequality. We also obtain topological and measure-theoretic consequences for quasiregular mappings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received: 26 June 2001; in final form: 14 January 2002/Published online: 5 September 2002

Rights and permissions

Reprints and permissions

About this article

Cite this article

Balogh, Z., Tyson, J. Polar coordinates in Carnot groups. Math. Z. 241, 697–730 (2002). https://doi.org/10.1007/s00209-002-0441-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-002-0441-7

Navigation