Curvature estimates for properly immersed ϕ_h-bounded submanifolds

2012/11/26 by G. Pacelli Bessa, Bessa, G. Pacelli, Barnabé Pessoa Lima +4
Mathematics · #53C42 (Primary) 35B50 (Secondary) #Advanced Harmonic Analysis Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG #msc:35B50 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1211.5910

Latex, 26 pages

arxiv created 2012/11/26 · openalex publication_date 2012/11/26 · arxiv updated 2012/11/27 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

Jorge-Koutrofiotis and Pigola-Rigoli-Setti proved sharp sectional curvature estimates for extrinsically bounded submanifolds. Alias, Bessa and Montenegro showed that these estimates hold on properly immersed cylindrically bounded submanifolds. On the other hand, Alias, Bessa and Dajczer proved sharp mean curvature estimates for properly immersed cylindrically bounded submanifolds. In this paper we prove these sectional and mean curvature estimates for a larger class of submanifolds, the properly immersed ϕ-bounded submanifolds.

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