English

A New Conformal Invariant for four-Dimensional Hypersurfaces

Differential Geometry 2023-11-20 v3

Abstract

A new conformally invariant energy for four-dimensional hypersurfaces is devised. It renders possible the study of a large class of curvature energies, and we show that their critical points are smooth. As corollaries, we obtain the regularity of the critical points of the four-dimensional analogues of the Willmore energy, of the QQ-curvature energy, but also that Bach-flat hypersurfaces are smooth, along with relevant estimates.

Keywords

Cite

@article{arxiv.2209.12469,
  title  = {A New Conformal Invariant for four-Dimensional Hypersurfaces},
  author = {Yann Bernard},
  journal= {arXiv preprint arXiv:2209.12469},
  year   = {2023}
}

Comments

Too many errors. To be redone elsewhere

R2 v1 2026-06-28T02:04:46.778Z