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Vietnam Journal of Mathematics 34:3(2006) 307-316

 Polar Coordinates on H-type Groups and Applications

Junqiang Han and Pengcheng Niu

Abstract.  In this paper we construct polar coordinates on H-type groups. As applications, we explicitly compute the volume of the ball in the sense of the distance and the constant in the fundamental solution of p-sub-Laplacian on the H-type group. Also, we prove some nonexistence results of weak solutions for a degenerate elliptic inequality on the H-type group.

2000 Mathematics Subject Classification: 35R45, 35J70.

Keywords: H-type group, polar coordinate, nonexistence, degenerate elliptic inequality.

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Published by Springer since January 2013