English

SL(n) covariant matrix-valued valuations on Lp-spaces

Differential Geometry 2024-08-14 v1

Abstract

A complete classification is established for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx). The assumption of matrix symmetry is eliminated. For n>2, such valuation is uniquely characterized by the moment matrix of measurable function. In the 2-dimensional case, while the rotation matrix shows up.

Keywords

Cite

@article{arxiv.2408.06835,
  title  = {SL(n) covariant matrix-valued valuations on Lp-spaces},
  author = {Chunna Zeng and Yu Lan},
  journal= {arXiv preprint arXiv:2408.06835},
  year   = {2024}
}