Relative Lorentzian volume comparison with integral Ricci and scalar curvature bound
نویسندگان
چکیده
منابع مشابه
Uniqueness of Ricci Flow Solution on Non-compact Manifolds and Integral Scalar Curvature Bound
of the Dissertation Uniqueness of Ricci Flow Solution on Non-compact Manifolds and Integral Scalar Curvature Bound
متن کاملA Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
Copyright q 2010 Zisheng Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound...
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In this paper we shall generalize the Bishop-Gromov relative volume comparison estimate to a situation where one only has an integral bound for the part of the Ricci curvature which lies below a given number. This will yield several compactness and pinching theorems.
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We prove the existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds provided there are barriers.
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In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota’s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2011
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2011.02.005