2011/04/30 by Debora Impera
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Applied mathematics #Bounded function #Curvature #Function (biology) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hessian matrix #Laplace operator #Mathematical analysis #Mathematical optimization #Mathematics #Maximum principle #Mean curvature #Optimal control #Order (exchange) #Physics #Pure mathematics #Ricci curvature #Scalar curvature #Sectional curvature #Spacetime #math.DG
paper · pdf · doi:10.1016/j.geomphys.2011.11.004
23 pages. Final version. To appear on Journal of Geometry and Physics
arxiv created 2011/11/08 · openalex publication_date 2011/11/13 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we prove Hessian and Laplacian comparison theorems for the Lorentzian distance function in a spacetime with sectional (or Ricci) curvature bounded by a certain function by means of a comparison criterion for Riccati equations. Using these results, under suitable conditions, we are able to obtain some estimates on the higher order mean curvatures of spacelike hypersurfaces satisfying a Omori-Yau maximum principle for certain elliptic operators.