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Currently displaying 1 – 2 of 2

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Brunn-Minkowski and isoperimetric inequality in the Heisenberg group.

Monti, Roberto — 2003

Annales Academiae Scientiarum Fennicae. Mathematica

Some properties of Carnot-Carathéodory balls in the Heisenberg group

Roberto Monti — 2000

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. $|\nabla_{H^{n}} d (z, t)| = 1$ in the classical sense for all $(z, t) \in H^{n}$ with $z \neq 0$ , where $d$ is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.

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