Curvature estimates for minimal hypersurfaces in singular spaces
β Scribed by Ulrich Dierkes
- Publisher
- Springer-Verlag
- Year
- 1995
- Tongue
- English
- Weight
- 746 KB
- Volume
- 122
- Category
- Article
- ISSN
- 0020-9910
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## Abstract Let__M__ be a complete nonβcompact stable minimal hypersurface in a locally symmetric space __N__ of nonnegative Ricci curvature. We prove that if the integral of square norm of the second fundamental form is finite, i.e., β«~__M__~ |__A__ |^2^ __dv__ < β, then __M__ must be totally geo
We establish extremality of Riemannian metrics g with non-negative curvature operator on symmetric spaces M = G/K of compact type with rk Grk K 1. Let αΈ‘ be another metric with scalar curvature ΞΊ, such that αΈ‘ g on 2-vectors. We show that ΞΊ ΞΊ everywhere on M implies ΞΊ = ΞΊ. Under an additional conditio