The Experts below are selected from a list of 39294 Experts worldwide ranked by ideXlab platform
Xuezhang Chen - One of the best experts on this subject based on the ideXlab platform.
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the Scalar Curvature flow on s n perturbation theorem revisited
Inventiones Mathematicae, 2012Co-Authors: Xuezhang ChenAbstract:For the problem of finding a geometry on S n , for n≥3, with a prescribed Scalar Curvature, there is a well-known result which is called the perturbation theorem; it is due to Chang and Yang (Duke Math. J. 64, 27–69, 1991). Their key assumption is that the candidate f for the prescribed Scalar Curvature is sufficiently near the Scalar Curvature of the standard metric in the sup norm. It is important to know how large that difference in sup norm can possibly be. Here we consider prescribing Scalar Curvature problem using the Scalar Curvature flow.
Zhiqin Lu - One of the best experts on this subject based on the ideXlab platform.
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normal Scalar Curvature conjecture and its applications
Journal of Functional Analysis, 2011Co-Authors: Zhiqin LuAbstract:Abstract In this paper, we proved the Normal Scalar Curvature Conjecture and the Bottcher–Wenzel Conjecture. We developed a new Bochner formula and it becomes useful with the first conjecture we proved. Using the results, we established some new pinching theorems for minimal submanifolds in spheres.
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proof of the normal Scalar Curvature conjecture
arXiv: Differential Geometry, 2007Co-Authors: Zhiqin LuAbstract:In this paper, we proved the normal Scalar Curvature conjecture and the Bottcher-Wenzel conjecture.
Jacopo Stoppa - One of the best experts on this subject based on the ideXlab platform.
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k stability of constant Scalar Curvature kahler manifolds
Advances in Mathematics, 2009Co-Authors: Jacopo StoppaAbstract:Abstract We show that a polarised manifold with a constant Scalar Curvature Kahler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S.K. Donaldson.
Frank Pacard - One of the best experts on this subject based on the ideXlab platform.
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blowing up and desingularizing constant Scalar Curvature kahler manifolds
Acta Mathematica, 2006Co-Authors: Claudio Arezzo, Frank PacardAbstract:This paper is concerned with the existence of constant Scalar Curvature Kahler metrics on blow-ups at finitely many points of compact manifolds which already carry constant Scalar Curvature Kahler metrics. We also consider the desingularization of isolated quotient singularities of compact orbifolds which carry constant Scalar Curvature Kahler metrics.
Yuxin Dong - One of the best experts on this subject based on the ideXlab platform.
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rigidity theorems for complete sasakian manifolds with constant pseudo hermitian Scalar Curvature
Journal of Geometric Analysis, 2017Co-Authors: Yibin Ren, Hezi Lin, Yuxin DongAbstract:The orthogonal decomposition of the Webster Curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenbock formulas for the traceless pseudo-Hermitian Ricci tensor of Sasakian manifolds with constant pseudo-Hermitian Scalar Curvature and the Chern–Moser tensor of the Sasakian pseudo-Einstein manifolds, respectively. By means of either subelliptic estimates or maximum principle, some rigidity theorems are established to characterize Sasakian pseudo-Einstein manifolds among Sasakian manifolds with constant pseudo-Hermitian Scalar Curvature and Sasakian space forms among Sasakian pseudo-Einstein manifolds, respectively.
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rigidity theorems for complete sasakian manifolds with constant pseudo hermitian Scalar Curvature
arXiv: Differential Geometry, 2014Co-Authors: Yuxin Dong, Hezi Lin, Yibin RenAbstract:The orthogonal decomposition of the Webster Curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenb\"ock formulas for the traceless pseudo-Hermitian Ricci tensor and the Chern-Moser tensor of Sasakian manifolds with constant pseudo-Hermitian Scalar Curvature and Sasakian pseudo-Einstein manifolds respectively. By means of either subelliptic estimates or maximum principle, some rigidity theorems are established to characterize Sasakian pseudo-Einstein manifolds among Sasakian manifolds with constant pseudo-Hermitian Scalar Curvature and Sasakian space forms among Sasakian pseudo-Einstein manifolds respectively.
