In this paper, the authors give a new proof of Block and Weinberger’s Bochner vanishing theorem built on direct computations in the K-theory of the localization algebra.
These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness prop...These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness properties. They also discuss several open problems and questions in the field.展开更多
Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold,the authors show that the connected sum M#W admits no complete metric of positive scalar curvature.When W=T...Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold,the authors show that the connected sum M#W admits no complete metric of positive scalar curvature.When W=T^(n),this provides a positive answer to the generalized Geroch conjecture in the spin setting.展开更多
基金This work was supported by the National Natural Science Foundation of China(Nos.11811530291,11831006,11771092)。
文摘In this paper, the authors give a new proof of Block and Weinberger’s Bochner vanishing theorem built on direct computations in the K-theory of the localization algebra.
文摘These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness properties. They also discuss several open problems and questions in the field.
基金supported by the National Natural Science Foundation of China(Nos.11931007,12101361)the Nankai Zhide Foundationthe project of Young Scholars of SDU and the Fundamental Research Funds of SDU(No.2020GN063)。
文摘Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold,the authors show that the connected sum M#W admits no complete metric of positive scalar curvature.When W=T^(n),this provides a positive answer to the generalized Geroch conjecture in the spin setting.
