## Duke Mathematical Journal

### Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type

#### Abstract

In this paper we study positive solutions to the CR Yamabe equation on groups of Heisenberg type. For the subclass of groups of Iwasawa type, we characterize those solutions that have partial symmetry, that is, those that are invariant with respect to the action of the orthogonal group in the first layer of the Lie algebra.

#### Article information

Source
Duke Math. J., Volume 106, Number 3 (2001), 411-448.

Dates
First available in Project Euclid: 13 August 2004

https://projecteuclid.org/euclid.dmj/1092403938

Digital Object Identifier
doi:10.1215/S0012-7094-01-10631-5

Mathematical Reviews number (MathSciNet)
MR1813232

Zentralblatt MATH identifier
1012.35014

#### Citation

Garofalo, Nicola; Vassilev, Dimiter. Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type. Duke Math. J. 106 (2001), no. 3, 411--448. doi:10.1215/S0012-7094-01-10631-5. https://projecteuclid.org/euclid.dmj/1092403938

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• \lccG. Lu \and J. Wei, On positive entire solutions to the Yamabe-type problem on the Heisenberg and stratified groups, Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 83–89.
• \lccJ. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304\hs–318.
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