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Journal of Convex Analysis 26 (2019), No. 4, 1349--1372
Copyright Heldermann Verlag 2019

Starshaped and Convex Sets in Carnot Groups and in the Geometries of Vector Fields

Federica Dragoni
School of Mathematics, Cardiff University, Great Britain

Doaa Filali
School of Mathematics, Cardiff University, Great Britain

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.

Keywords: Starshaped, starlike, convex, Heisenberg group, Carnot group, sub-Riemannian, Hoermander condition, vector fields.

MSC: 35R03, 30C45, 32F17, 35E10

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