2022/09/26 by Yann Bernard, Bernard, Yann
Mathematics · Medicine · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Pelvic and Acetabular Injuries
paper · pdf · doi:10.48550/arxiv.2209.12469
openalex publication_date 2022/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.