刚性及谱纯量曲率的弱概念
Rigidity and weak notions of spectral scalar curvature
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中文总结 AI 辅助
本文通过二面角刚性结果，为谱纯量曲率从下方有界提出弱表述，并证明满足特定条件的度量必为平坦，受Gromov弱概念启发。
中文摘要 AI 辅助
我们通过建立二面角刚性结果，给出了谱纯量曲率从下方有界的弱表述。给定某个特殊的凸多面体，若另一度量在内部具有非负谱纯量曲率，具有加权平均凸的面，且其沿棱的二面角处处小于或等于其平坦多面体模型中的对应值，则该度量必为平坦的。此研究受Gromov关于非负纯量曲率弱概念定义的启发。
英文摘要
We give a weak formulation of spectral scalar curvature bounded from below via establishing a dihedral rigidity result. Given some special convex polyhedron, if another metric are of non-negative spectral scalar curvature in the interior, with weighted mean-convex faces, and with its dihedral angles less than or equal to their flat polyhedral model everywhere along the edges, then the metric must be flat. This is motivated by Gromov's definition of a weak notion of non-negative scalar curvature.
发表机构
- Central China Normal University（华中师范大学）
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