关于Ricci流和量子势的几点注记

作为Ricci流的量子虫洞

Quantum wormhole as a Ricci flow

我们认为时空泡沫中的量子虫洞可以用里奇流来描述。在这种解释中，Ricci流是一个统计系统，Ricci流中的每个度量都是微观状态。微观状态的概率密度与重新标度的Ricci流的Perelman泛函有关。

Harmonic spinors in the Ricci flow

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 exoti…