Ends of Gradient Ricci Solitons
Ends of Gradient Ricci Solitons
复制标题
DOI：
10.1007/s12220-022-01047-2
复制
发表时间：
2022-09
期刊：
影响因子：
--
通讯作者：
Ovidiu Munteanu;Jiaping Wang
中科院分区：
文献类型：
--
作者：
Ovidiu Munteanu;Jiaping Wang
Ricci流的自相似解，称为Ricci孤子，是重要的几何对象。为了解决是否可以通过连通和从现有孤子构造新孤子的问题，我们研究了孤子在无穷远处的连通性问题。本文简要介绍了我们在这方面所做的工作以及新的结果。新的结果表明，如果n维梯度收缩Ricci孤子的标量曲率在下界，则它必然在无穷远处相连。
Self-similar solutions to Ricci flows, called Ricci solitons, are important geometric objects. To address the question whether new solitons can be constructed from existing ones through connected sums, we are led to investigate the issue of connectedness at infinity for solitons. The paper provides a brief account of our work along this line as well as a new result. The new result says that ann-dimensional gradient shrinking Ricci soliton is necessarily connected at infinity if its scalar curvature is bounded above by