论文标题
渐近的欧几里得Ricci流动的旋转能量
The spinorial energy for asymptotically Euclidean Ricci flow
论文作者
论文摘要
本文介绍了Perelman的加权Hilbert-Einstein动作和旋转器的Dirichlet Energy的功能性推广。它在一系列的非紧密歧管上定义明确。在渐近的欧几里得歧管上，该功能被证明可以接收一个独特的临界点，该点必须具有最小最大的类型，而RICCI流量是其梯度流。该证明基于加权旋转功能的变异公式，对所有带边界的旋转歧管有效。
This paper introduces a functional generalizing Perelman's weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well-defined on a wide class of non-compact manifolds; on asymptotically Euclidean manifolds, the functional is shown to admit a unique critical point, which is necessarily of min-max type, and Ricci flow is its gradient flow. The proof is based on variational formulas for weighted spinorial functionals, valid on all spin manifolds with boundary.
