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Euclidean rectifiability of sub-Finsler spheres in free-Carnot groups of step 2
Published 15 Mar 2024 in math.MG and math.OC | (2403.10196v1)
Abstract: We consider 2-step free-Carnot groups equipped with sub-Finsler distances. We prove that the metric spheres are codimension-one rectifiable from the Euclidean viewpoint. The result is obtained by studying how the Lipschitz constant for the distance function behaves near abnormal geodesics.
- A Sub-Finsler Problem on the Cartan Group. Proc. Steklov Inst. Math., 304:42 – 59, 2017.
- Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions. Journal of Dynamical and Control Systems, 23:547 – 575, 2019.
- R. Benedetti and J. Risler. Real algebraic and semi-algebraic sets. Actualites mathematiques. Hermann, 1990.
- The Sard problem in step 2 and in filiform Carnot groups. ESAIM: Control, Optimisation and Calculus of Variations, 28, 2022.
- E. Breuillard and E. Le Donne. On the rate of convergence to the asymptotic cone for nilpotent groups and subFinsler geometry. Proceedings of the National Academy of Sciences of the United States of America, 110(48):19220 – 19226, 2013.
- H. Federer. Geometric measure theory. Classics in mathematics. Springer, 1996.
- A. Figalli and L. Rifford. Mass Transportation on Sub-Riemannian Manifolds. Geometric and Functional Analysis, 20:124 – 159, 2010.
- E. Hakavuori and E. Le Donne. Blowups and blowdowns of geodesics in Carnot groups. Journal of Differential Geometry, 123(2):267 – 310, 2023.
- E. Le Donne and S. Nicolussi Golo. Regularity properties of spheres in homogeneous groups. Transactions of the American Mathematical Society, 370:2057 – 2084, 2016.
- R. Montgomery. A Tour of Subriemannian Geometries, Their Geodesics and Applications, volume 91 of Mathematical Surveys and Monographs. American Mathematical Society, 2002.
- Sard property for the endpoint map on some Carnot groups. Ann. Inst. H. Poincaré, Anal. Non Linéaire 33(6):1639 – 1666, 2016.
- A. Ottazzi and D. Vittone. On the codimension of the abnormal set in step two Carnot groups. ESAIM: Control, Optimisation and Calculus of Variations, 25, 2019.
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