Higher order mean curvature estimates for bounded complete hypersurfaces
L. J. Alias, M. Dajczer, M. Rigoli
TL;DR
This paper derives precise estimates for higher order mean curvatures of complete bounded hypersurfaces in Riemannian and Lorentzian manifolds, advancing geometric analysis in these contexts.
Contribution
It provides sharp curvature estimates for hypersurfaces in both Riemannian and Lorentzian settings, extending previous results to higher order mean curvatures.
Findings
Sharp estimates for higher order mean curvatures of hypersurfaces.
Results applicable to both Riemannian and Lorentzian ambient spaces.
Enhanced understanding of geometric properties of complete hypersurfaces.
Abstract
We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient spaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research