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PreprintCC BY 4.0arXiv

Lp-Integral Affine Surface Area-Variational Capacity Inequalities

  • Yibin Feng
  • Ding Zhang
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Abstract

For n≥ 2 and 1<p<n, Ludwig-Xiao-Zhang \cite{LXYZ} asked whether the Lp-integral affine surface area of every convex body containing the origin in its interior is bounded above by the ball-normalized multiple of Lp-variational capacity, and whether the analogous analytic inequality holds for Lp-convexified level sets. We answer both questions negatively.

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Cite

BibTeXRIS
BibTeX
@misc{feng2026lpintegral,
  title = {{$L_p$-Integral Affine Surface Area-Variational Capacity Inequalities}},
  author = {Yibin Feng and Ding Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13957},
  eprint = {2610.13957},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13957},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - L_p-Integral Affine Surface Area-Variational Capacity Inequalities
AU  - Yibin Feng
AU  - Ding Zhang
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.13957
UR  - https://arxiv.org/abs/2610.13957
AB  - For n≥ 2 and 1<p<n, Ludwig-Xiao-Zhang \cite{LXYZ} asked whether the L_p-integral affine surface area of every convex body containing the origin in its interior is bounded above by the ball-normalized multiple of L_p-variational capacity, and whether the analogous analytic inequality holds for L_p-convexified level sets. We answer both questions negatively.
ER  -