Some constructions of formally self-adjoint conformally covariant polydifferential operators

We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions of families of such operators. In one direction, we show that any homogeneous conformally variational scalar Riemannian invariant (CVI) induces one of these operators. In another direction, we use the ambient metric to give alternative constructions of certain operators produced this way, one of which is a formally self-adjoint, fourth-order, conformally covariant tridifferential operator which should be regarded as the simplest fully nonlinear analogue of the Paneitz operator.

Files

Metadata

Work Title Some constructions of formally self-adjoint conformally covariant polydifferential operators
Access
Open Access
Creators
  1. Jeffrey S. Case
  2. Yueh Ju Lin
  3. Wei Yuan
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Publisher
  1. Advances in Mathematics
Publication Date June 4, 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.1016/j.aim.2022.108312
Deposited January 06, 2025

Versions

Analytics

Collections

This resource is currently not in any collection.

Work History

Version 1
published

  • Created
  • Added 2002.05874-1.pdf
  • Added Creator Jeffrey S. Case
  • Added Creator Yueh Ju Lin
  • Added Creator Wei Yuan
  • Published
  • Updated