论文标题
加权歧管上的纺纱器和质量
Spinors and mass on weighted manifolds
论文作者
论文摘要
本文将经典的自旋几何形状概括为加权歧管的设置（具有密度的歧管），并为RICCI流提供了应用。 Perelman引入的自然相关加权式操作员的光谱特性及其与加权标量曲率的关系。此外，定义了对渐近的欧几里得（AE）歧管的ADM质量的概括。在具有非负重标量曲率的歧管上，它满足加权的witten公式，从而满足正加权质量定理。最后，在这种歧管上，RICCI流量是所述加权ADM质量的梯度流，是自然选择权重功能。这产生了一个单调性公式，用于沿RICCI流量的加权旋转旋转器的加权旋转Dirichlet能量。
This paper generalizes classical spin geometry to the setting of weighted manifolds (manifolds with density) and provides applications to the Ricci flow. Spectral properties of the naturally associated weighted Dirac operator, introduced by Perelman, and its relationship with the weighted scalar curvature are investigated. Further, a generalization of the ADM mass for weighted asymptotically Euclidean (AE) manifolds is defined; on manifolds with nonnegative weighted scalar curvature, it satisfies a weighted Witten formula and thereby a positive weighted mass theorem. Finally, on such manifolds, Ricci flow is the gradient flow of said weighted ADM mass, for a natural choice of weight function. This yields a monotonicity formula for the weighted spinorial Dirichlet energy of a weighted Witten spinor along Ricci flow.
