Notions of Convexity in Carnot Groups

CONTENTS 1. Introduction 2. Preliminaries 3. Strongly convex functions: A notion to abandon 4. Mildly convex functions: The appearance of horizontal planes 5. Weakly convex functions: The horizontal Hessian 6. Weak convexity of the gauge in groups of Heisenberg type 7. Convexity of sets 8. Further properties of second derivatives of weakly convex functions 9. Basic properties of first derivatives of weakly convex functions: L

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