Curvature estimates for graphs in warped products
Alexandre Paiva Barreto, Fabiani A. Coswosck, Luiz Hartmann
TL;DR
This paper establishes upper bounds for curvature-related quantities of graphs in warped product spaces, providing insights into geometric properties and applications to pseudo-hyperbolic spaces and space forms.
Contribution
It introduces new curvature estimates for graphs in warped products, advancing understanding of their geometric behavior and applications.
Findings
Upper bounds for mean curvature, scalar curvature, and shape operator norm
Applications to pseudo-hyperbolic spaces and space forms
Enhanced understanding of geometric properties of graphs in warped products
Abstract
We prove local and global upper estimates for the infimum of the mean curvature, the scalar curvature and the norm of the shape operator of graphs in a warped product space. Using these estimates, we obtain some results on pseudo-hyperbolic spaces and space forms.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research