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2 results

  • On almost quotient Yamabe solitons

  • Part of
  • Willian Tokura, Marcelo Barboza, Elismar Batista, Priscila Kai
  • Journal:
    Glasgow Mathematical Journal / Volume 66 / Issue 3 / September 2024
    Published online by Cambridge University Press:
    11 April 2024, pp. 479-493
    Print publication:
    September 2024
    • Article
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  • In this paper, we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call almost quotient Yamabe solitons as they extend quite naturally those already called quotient Yamabe solitons. We present sufficient conditions for a compact almost quotient Yamabe soliton to be either trivial or isometric with an Euclidean sphere. We also characterize noncompact almost gradient quotient Yamabe solitons satisfying certain conditions on both its Ricci tensor and potential function.

  • Bounded rigidity of manifolds and asymptotic dimension growth

  • Stanley S. Chang, Steven Ferry, Guoliang Yu
  • Journal:
    Journal of K-Theory / Volume 1 / Issue 1 / February 2008
    Published online by Cambridge University Press:
    07 January 2008, pp. 129-144
    Print publication:
    February 2008

  • We provide a bounded rigidity result for uniformly contractible manifolds with bounded geometry and sufficiently slow asymptotic dimension growth. This notion of asymptotic growth is a generalization of Gromov's definition of asymptotic dimension. In particular for these manifolds we prove that the bounded assembly map is an isomorphism. Our result is inspired by the coarse Baum-Connes results of Yu and the development of squeezing structures.