Abstract

The paper gives an overview on convex sets and starshaped sets in Carnot groups and in the more general case of geometries of vector fields, including in particular the Hoermander case. We develop some new notions and investigate their mutual relations and properties.

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Keywords

  • Starshaped
  • starlike
  • convex
  • Heisenberg group
  • Carnot group
  • sub-Riemannian
  • Hörmander condition
  • vector fields

Mathematics Subject Classification

35R03, 30C45, 32F17, 35E10

Suggested citation

F. Dragoni, D. Filali. “Starshaped and Convex Sets in Carnot Groups and in the Geometries of Vector Fields.” Journal of Convex Analysis 26 (2019), No. 4, 1349–1372. https://doi.org/10.68381/jca26072

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press.