Balogh, Z.M., Kristály, A. & Sipos, K. (2018) Calculus of Variations and Partial Differential Equations [Matematică, Q1]

Publicat: 24 Noiembrie 2020

Balogh, Z.M., Kristály, A. & Sipos, K. (2018) Geometric inequalities on Heisenberg groups. Calculus of Variations and Partial Differential Equations, 57(2), 61.

DOI: https://doi.org/10.1007/s00526-018-1320-3

✓ Publisher: Springer
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics, Applied; Mathematics
✓ Article Influence Score (AIS): 1.837 (2018) / Q1 in all categories

Abstract: We establish geometric inequalities in the sub-Riemannian setting of the Heisenberg group H-n. Our results include a natural sub-Riemannian version of the celebrated curvature-dimension condition of Lott-Villani and Sturm and also a geodesic version of the Borell-Brascamp-Lieb inequality akin to the one obtained by Cordero-Erausquin, McCann and Schmuckenschlager. The latter statement implies sub-Riemannian versions of the geodesic Prekopa-Leindler and Brunn-Minkowski inequalities. The proofs are based on optimal mass transportation and Riemannian approximation of Hn developed by Ambrosio and Rigot. These results refute a general point of view, according to which no geometric inequalities can be derived by optimal mass transportation on singular spaces.

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