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.
