Geodesic
Loomis–Whitney inequalities on corank 1 Carnot groups
Ye Zhang1
1Okinawa Institute of Science and Technology Graduate University, Analysis on Metric Spaces Unit
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 437–459

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In this paper we provide another way to deduce the Loomis–Whitney inequality on higher dimensional Heisenberg groups $\mathbb{H}^n$ based on the one on the first Heisenberg group $\mathbb{H}^1$ and the known nonlinear Loomis–Whitney inequality (which has more projections than ours). Moreover, we generalize the result to the case of corank 1 Carnot groups and products of such groups. Our main tool is the modified equivalence between the Brascamp–Lieb inequality and the subadditivity of the entropy developed in Carlen and Cordero-Erausquin (2009).
DOI : 10.54330/afm.146800
Keywords: Corank 1 Carnot group, Loomis–Whitney inequality, Brascamp–Lieb inequality, entropy, Sobolev inequality, isoperimetric inequality

Ye Zhang  1

1 Okinawa Institute of Science and Technology Graduate University, Analysis on Metric Spaces Unit 
Ye Zhang. Loomis–Whitney inequalities on corank 1 Carnot groups. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 437–459. doi: 10.54330/afm.146800
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