PreprintCC0arXiv
A very short unified proof of Dar's conjecture and Log-Brunn--Minkowski in the plane
Abstract
This short note gives a very short unified proof of both Dar's conjecture and the log-Brunn--Minkowski inequality in the plane. A planar Lp-Brunn-Minkowski inequality for p∈ [−∞,0] is established and gives the two key inequalities at p=0 and p=−∞. Motivated by this new proof, the author proposes a related conjecture in tr3, to attack the two conjectures in higher dimensions.
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BibTeX
@misc{xi2026very,
title = {{A very short unified proof of Dar's conjecture and Log-Brunn--Minkowski in the plane}},
author = {Dongmeng Xi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08495},
eprint = {2609.08495},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08495},
note = {CC0},
}
RIS
TY - UNPB
TI - A very short unified proof of Dar's conjecture and Log-Brunn--Minkowski in the plane
AU - Dongmeng Xi
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08495
UR - https://arxiv.org/abs/2609.08495
AB - This short note gives a very short unified proof of both Dar's conjecture and the log-Brunn--Minkowski inequality in the plane. A planar L_p-Brunn-Minkowski inequality for p∈ [−∞,0] is established and gives the two key inequalities at p=0 and p=−∞. Motivated by this new proof, the author proposes a related conjecture in tr^3, to attack the two conjectures in higher dimensions.
ER -