论文标题
RICCI流中的谐波旋转器
Harmonic spinors in the Ricci flow
论文作者
论文摘要
本文研究了封闭的歧管上的RICCI流动，该流量承认谐波旋转器。结果表明，Perelman的Ricci流熵可以用在所有维度上的谐波旋转器的能量来表达，并在四个维度上以Seiberg-witten单极的能量来表达。因此，RICCI流量是这些能量的梯度流。证明依赖于此处介绍的单极方程的加权版本。此外，事实证明，尖锐的抛物线寄托式Hitchin-thorpe不平等现象，旋转4个manifolds。因此，因此，任何外来K3表面上的归一化RICCI流都必须变得单数。
This paper studies the Ricci flow on closed manifolds admitting harmonic spinors. It is shown that Perelman's Ricci flow entropy can be expressed in terms of the energy of harmonic spinors in all dimensions, and in four dimensions, in terms of the energy of Seiberg-Witten monopoles. Consequently, Ricci flow is the gradient flow of these energies. The proof relies on a weighted version of the monopole equations, introduced here. Further, a sharp parabolic Hitchin-Thorpe inequality for simply-connected, spin 4-manifolds is proven. From this, it follows that the normalized Ricci flow on any exotic K3 surface must become singular.
