Some properties of Carnot-Carathéodory balls in the Heisenberg group
Monti, Roberto
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000), p. 155-167 / Harvested from Biblioteca Digitale Italiana di Matematica
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Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. ∇Hn⁡d⁢z,t=1 in the classical sense for all z,t∈Hn with z≠0, where d is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.

Usando la rappresentazione esatta per le sfere di Carnot-Carath´ eodory nel gruppo di Heisenberg, proviamo che: 1. ∇Hn⁡d⁢z,t=1 in senso classico per ogni z,t∈Hn con z≠0, dove d è la distanza dall’origine; 2. Le sfere metriche non sono insiemi isoperimetrici ottimali nel gruppo di Heisenberg.

Publié le : 2000-09-01
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     author = {Roberto Monti},
     title = {Some properties of Carnot-Carath\'eodory balls in the Heisenberg group},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {11},
     year = {2000},
     pages = {155-167},
     zbl = {1197.53064},
     mrnumber = {1841689},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2000_9_11_3_155_0}
}

Monti, Roberto. Some properties of Carnot-Carathéodory balls in the Heisenberg group. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000) pp. 155-167. http://gdmltest.u-ga.fr/item/RLIN_2000_9_11_3_155_0/

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