English

A positive solution to the $L^p$ projection centroid conjecture

Metric Geometry 2026-05-21 v1

Abstract

In a classical paper [20] in 2000, Lutwak-Yang-Zhang established the LpL^p analog of the Petty projection inequality and the LpL^p analog of the Busemann-Petty centroid inequality. In Section 7 of [20], Lutwak-Yang-Zhang proposed the important LpL^p projection centroid conjecture. We give a positive solution to the LpL^p projection centroid conjecture in this work.

Cite

@article{arxiv.2605.20840,
  title  = {A positive solution to the $L^p$ projection centroid conjecture},
  author = {Jin Dai and Tuo Wang},
  journal= {arXiv preprint arXiv:2605.20840},
  year   = {2026}
}