Jacobian determinant inequality on corank 1 Carnot groups with applications

Balogh, Zoltán M.; Kristály, Alexandru; Sipos, Kinga (2019). Jacobian determinant inequality on corank 1 Carnot groups with applications. Journal of functional analysis, 277(12), p. 108293. Elsevier 10.1016/j.jfa.2019.108293

	Text 1-s2.0-S0022123619302629-main.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (701kB) | Request a copy
Preview	Text 1701.08831.pdf - Accepted Version Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works (CC-BY-NC-ND). Download (639kB) | Preview

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, McCann and Schmuckenschläger. 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.

Interest & Impact

Downloads

10 since deposited on 24 Oct 2019
6 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item