A New Conformal Invariant for four-Dimensional Hypersurfaces

Yann Bernard

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arXiv · 2209.12469

A New Conformal Invariant for four-Dimensional Hypersurfaces

Yann Bernard

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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 $Q$-curvature energy, but also that Bach-flat hypersurfaces are smooth, along with relevant estimates.

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Yann Bernard. 2022-09-26. A New Conformal Invariant for four-Dimensional Hypersurfaces. https://arxiv.org/abs/2209.12469

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