2012/10/21 by Erwann Aubry, Aubry, Erwann, Jean-François Grosjean +2
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG
paper · pdf · doi:10.48550/arxiv.1210.5690
arxiv created 2012/10/21 · openalex publication_date 2012/10/21 · arxiv updated 2012/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that Euclidean hypersurfaces with almost extremal extrinsic radius or λ1 have a spectrum that asymptotically contains the spectrum of the extremal sphere in the Reilly or Hasanis-Koutroufiotis Inequalities. We also consider almost extremal hypersurfaces which satisfy a supplementary bound on vM‖\B‖αn and show that their spectral and topological properties depends on the position of α with respect to the critical value dim M. The study of the metric shape of these extremal hypersurfaces will be done in \citeAG1, using estimates of the present paper.