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Stability of Hyperplane Projections of the Regular Simplex and Lp-Projection Bodies of balls in ℓqn(ℝ)

  • Jacek Jakimiuk
  • Christos Pandis
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Abstract

We prove stability estimates for extremal hyperplane projections of the regular simplex. We further generalize the analogous stability estimates for ℓq-balls by the first named author and the monotonicity theorem for normalized ratios by Barthe and Naor to the Lp-setting. To this end, we derive closed formulas for the support functions of their Lp-projection bodies, complementing those obtained by the second named author. A key ingredient in our proofs is a stability refinement of the majorization inequality for Gaussian mixtures.

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Cite

BibTeXRIS
BibTeX
@misc{jakimiuk2026stability,
  title = {{Stability of Hyperplane Projections of the Regular Simplex and $L_p$-Projection Bodies of balls in $\ell_q^n(\mathbbR)$}},
  author = {Jacek Jakimiuk and Christos Pandis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23489},
  eprint = {2610.23489},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23489},
}
RIS
TY  - UNPB
TI  - Stability of Hyperplane Projections of the Regular Simplex and L_p-Projection Bodies of balls in ℓ_q^n(ℝ)
AU  - Jacek Jakimiuk
AU  - Christos Pandis
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23489
UR  - https://arxiv.org/abs/2610.23489
AB  - We prove stability estimates for extremal hyperplane projections of the regular simplex. We further generalize the analogous stability estimates for ℓ_q-balls by the first named author and the monotonicity theorem for normalized ratios by Barthe and Naor to the L_p-setting. To this end, we derive closed formulas for the support functions of their L_p-projection bodies, complementing those obtained by the second named author. A key ingredient in our proofs is a stability refinement of the majorization inequality for Gaussian mixtures.
ER  -