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- Title
A WEIGHTED QUANTITATIVE ISOPERIMETRIC INEQUALITY FOR KORÁNYI SPHERE IN HEISENBERG GROUP H<sup>n</sup>.
- Authors
GUOQING HE; PEIBIAO ZHAO
- Abstract
It is well known that the Korányi sphere w.r.t. the Korányi distance is not an isoperimetric set in Heisenbeg group Hn. In this paper, we investigate Korányi sphere in a Heisenberg group associated with a density |z|-(2n+1)e-a/|c| (a > 0), and derive a weighted isoperimetric inequality and a weighted quantitative isoperimetric inequality for Korányi spheres in half-cylinders. This note also shows that the Korányi sphere is the weighted isoperimetric set in the weighted Heisenberg group Hn.
- Subjects
HEISENBERG model; EULER equations; MATHEMATICS; VARIATIONAL inequalities (Mathematics); ISOPERIMETRIC inequalities
- Publication
Journal of Mathematical Inequalities, 2022, Vol 16, Issue 4, p1493
- ISSN
1846-579X
- Publication type
Article
- DOI
10.7153/jmi-2022-16-97