Balogh, Z.M., Kristaly, A. & Sipos, K. (2019) Journal of Functional Analysis [Matematică, Q1]

Publicat: 05 Noiembrie 2020

Balogh, Z.M., Kristaly, A. & Sipos, K. (2019) Jacobian determinant inequality on corank 1 Carnot groups with applications. Journal of Functional Analysis, 277(12), 108293

DOI: https://doi.org/10.1016/j.jfa.2019.108293

✓ Publisher: Elsevier
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics
✓ Article Influence Score (AIS): 1.653 (2019) / Q1

Abstract: We establish a weighted pointwise Jacobian determinant inequality on corank 1 Carnot groups related to optimal mass transportation akin to the work of Cordero-Erausquin, Mc-Cann and Schmuckenschlager. In this setting, the presence of abnormal geodesics does not allow the application of the general sub-Riemannian optimal mass transportation theory developed by Figalli and Rifford and we need to work with a weaker notion of Jacobian determinant. Nevertheless, our result achieves a transition between Euclidean and sub-Riemannian structures, corresponding to the mass transportation along abnormal and strictly normal geodesics, respectively. The weights appearing in our expression are distortion coefficients that reflect the delicate sub-Riemannian structure of our space. As applications, entropy, Brunn-Minkowski and Borell-Brascamp-Lieb inequalities are established on Carnot groups.

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