On positive entire solutions to the Yamabe-type problem on the Heisenberg and stratified groups

Authors:
Guozhen Lu and Juncheng Wei

Journal:
Electron. Res. Announc. Amer. Math. Soc. **3** (1997), 83-89

MSC (1991):
Primary 35H05; Secondary 35J70

Published electronically:
August 28, 1997

MathSciNet review:
1465830

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a nilpotent, stratified homogeneous group, and let , be left invariant vector fields generating the Lie algebra associated to . The main goal of this paper is to study the Yamabe type equations associated with the sub-Laplacian on :

Especially, we will establish the existence, nonexistence and asymptotic behavior of positive solutions to (0.1). Our results include the Yamabe type problem on the Heisenberg group as a special case, which is of particular importance and interest and also appears to be new even in this case.

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Additional Information

**Guozhen Lu**

Affiliation:
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435

Email:
gzlu@math.wright.edu

**Juncheng Wei**

Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong

Email:
wei@math.cuhk.edu.hk

DOI:
https://doi.org/10.1090/S1079-6762-97-00029-2

Keywords:
Heisenberg group,
stratified group,
Yamabe problem,
a priori estimates,
asymptotic behavior,
positive entire solutions

Received by editor(s):
June 12, 1997

Published electronically:
August 28, 1997

Additional Notes:
The work of the first author was supported in part by the National Science Foundation Grant #DMS96-22996.

The work of the second author was supported in part by an Earmarked Grant from RGC of Hong Kong.

Communicated by:
Thomas Wolff

Article copyright:
© Copyright 1997
American Mathematical Society