Calculus of Variations and Geometric Measure Theory

E. Hakavuori

Infinite geodesics and isometric embeddings in Carnot groups of step 2

created by hakavuori on 16 Mar 2020


Published Paper

Inserted: 16 mar 2020

Journal: SIAM Journal on Control and Optimization
Volume: 58
Number: 1
Pages: 447-461
Year: 2020

ArXiv: 1905.03214 PDF


In the setting of step 2 sub-Finsler Carnot groups with strictly convex norms, we prove that all infinite geodesics are lines. It follows that for any other homogeneous distance, all geodesics are lines exactly when the induced norm on the horizontal space is strictly convex. As a further consequence, we show that all isometric embeddings between such homogeneous groups are affine. The core of the proof is an asymptotic study of the extremals given by the Pontryagin Maximum Principle.

Tags: GeoMeG