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The Petty Conjecture for Convex Bodies of Revolution
Abstract
The Petty conjecture asserts that the quotient Vn(ΠK)/Vn(K)n−1 is minimized among all convex bodies precisely by ellipsoids. In this paper, we prove the conjecture for all convex bodies of revolution in ℝn, n≥3, including the equality cases.
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BibTeX
@misc{mielkesulz2026petty,
title = {{The Petty Conjecture for Convex Bodies of Revolution}},
author = {Florian Mielke-Sulz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13517},
eprint = {2609.13517},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13517},
}
RIS
TY - UNPB
TI - The Petty Conjecture for Convex Bodies of Revolution
AU - Florian Mielke-Sulz
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13517
UR - https://arxiv.org/abs/2609.13517
AB - The Petty conjecture asserts that the quotient V_n(ΠK)/V_n(K)^n−1 is minimized among all convex bodies precisely by ellipsoids. In this paper, we prove the conjecture for all convex bodies of revolution in ℝ^n, n≥3, including the equality cases.
ER -