On the inner cone property forconvex sets in two-step Carnot groups, with applications to monotone sets

• Autores: Daniele Morbidelli
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 2, 2020, págs. 391-421
• Idioma: inglés
• DOI: 10.5565/publmat6422002
• Enlaces
  • Texto completo  1    2  
• Resumen

  • 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.

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