This paper is devoted to a deep analysis of the process known as Cheeger deformation, applied to manifolds with isometric group actions. Here, we provide new curvature estimates near singular orbits and present several applications. As the main result, we answer a question raised by a seminal result of Searle–Wilhelm about lifting positive Ricci curvature from the quotient of an isometric action. To answer this question, we develop techniques that can be used to provide a substantially streamlined version of a classical result of Lawson and Yau, generalize a curvature condition of Chavéz, Derdzinski, and Rigas, as well as, give an alternative proof of a result of Grove and Ziller.

本文致力于深入分析称为 Cheeger 变形的过程，该过程应用于具有等距群作用的流形。在这里，我们提供了奇异轨道附近的新曲率估计并展示了几个应用。作为主要结果，我们回答了 Searle-Wilhelm 的开创性结果提出的关于从等距作用的商提升正 Ricci 曲率的问题。为了回答这个问题，我们开发的技术可用于提供 Lawson 和 Yau 的经典结果的基本简化版本，概括 Chavéz、Derdzinski 和 Rigas 的曲率条件，以及给出结果的替代证明格鲁夫和齐勒。