On the inner cone property forconvex sets in two-step Carnot groups, with applications to monotone sets
Morbidelli, Daniele (Università di Bologna. Dipartimento di Matematica)

Date:	2020
Abstract:	In the setting of two-step Carnot groups we show a "cone property" forhorizontally convex sets. Namely, we prove that, given a horizontally convex set C,a pair of points P ¬ C and Q ¬ int(C), both belonging to a horizontal line , thenan open truncated subRiemannian cone around and with vertex at P is containedin C. We apply our result to the problem of classification of horizontally monotone setsin Carnot groups. We are able to show that monotone sets in the direct product H×Rof the Heisenberg group with the real line have hyperplanes as boundaries.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Subriemannian distance ; Carnot groups ; Monotone sets
Published in:	Publicacions matemàtiques, Vol. 64 Núm. 2 (2020) , p. 391-421 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/371164
DOI: 10.5565/PUBLMAT6422002

31 p, 452.1 KB

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