标题： 哈密顿恒等式和完备梯度孤立子的刚性 显示英文标题

标题： Hamilton's identity and rigidity of complete gradient solitons

摘要： 在本工作中，我们研究梯度孤立子对一般的几何流。 我们的方法是理解为了扩展关于里奇孤立子的结果，需要对流做出哪些假设。 在这方面，我们确定了一个恒等式，该恒等式首次在理查德·哈密顿关于里奇孤立子的开创性工作中被利用，我们称之为哈密顿恒等式。 我们证明，对于任意几何流，该恒等式的版本允许恢复关于刚性、势函数的增长、体积增长以及欧莫里-亚最大原理的结果，这些结果已经在梯度里奇孤立子中被证明。 显示英文摘要

摘要： In this work, we study gradient solitons to general geometric flows. Our approach is to understand what assumptions need to be made about a flow in order to extend results about Ricci solitons. In this direction, we identify an identity, first exploited in the pioneering work of Richard Hamilton in the case of Ricci solitons, which we call Hamilton's identity. We show that a version of this identity for an arbitrary geometric flow allows one to recover results about rigidity, the growth of the potential function, volume growth and the Omori-Yau maximum principle that have been proven for gradient Ricci solitons.