PreprintarXiv licencearXiv
Ubiquity in the setting of forward-reverse Brascamp-Lieb inequalities
Abstract
The ubiquity of geometric Brascamp-Lieb data, which refers to a certain density property of geometric data within the set of all feasible Brascamp-Lieb data, has recently been studied. Motivated in part by a question of Bennett-Tao concerning a possible connection or analogue of the adjoint Brascamp-Lieb inequality to the forward-reverse Brascamp-Lieb inequality, we establish ubiquity in the forward-reverse setting. Our proof takes an analytic approach and, to overcome the difficulties arising in extending ubiquity to the forward-reverse setting, makes use of tools from the calculus of variations such as Danskin's theorem and Ekeland's variational principle.
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BibTeX
@misc{watanabe2026ubiquity,
title = {{Ubiquity in the setting of forward-reverse Brascamp-Lieb inequalities}},
author = {Mirei Watanabe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.26500},
eprint = {2606.26500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26500},
}
RIS
TY - UNPB
TI - Ubiquity in the setting of forward-reverse Brascamp-Lieb inequalities
AU - Mirei Watanabe
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2606.26500
UR - https://arxiv.org/abs/2606.26500
AB - The ubiquity of geometric Brascamp-Lieb data, which refers to a certain density property of geometric data within the set of all feasible Brascamp-Lieb data, has recently been studied. Motivated in part by a question of Bennett-Tao concerning a possible connection or analogue of the adjoint Brascamp-Lieb inequality to the forward-reverse Brascamp-Lieb inequality, we establish ubiquity in the forward-reverse setting. Our proof takes an analytic approach and, to overcome the difficulties arising in extending ubiquity to the forward-reverse setting, makes use of tools from the calculus of variations such as Danskin's theorem and Ekeland's variational principle.
ER -