Positive Ricci curvature through Cheeger deformations

• Cavenaghi, Leonardo F. ^[1] ; Silva, Renato J. M. e ^[2] ; Sperança, Llohann D. ^[3]
  1. [1] Instituto de Matemática, Estatística e Computação Cinetífica – Unicamp, Rua Sérgio Buarque de Holanda, 651, Campinas, SP, 13083-859, Brazil
  2. [2] Instituto de Matemática, Estatística e Computação Científica – UNICAMP, Rua Sérgio Buarque de Holanda, 651, Campinas, SP, 13083-97, Brazil
  3. [3] Instituto de Ciência e Tecnologia – Unifesp, Avenida Cesare Mansueto Giulio Lattes, 1201, São José dos Campos, SP, 12247-014, Brazil

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 2, 2024, págs. 481-510
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.