Corpus ID: 1907699

Collapsed Riemannian manifolds with bounded sectional curvature

  title={Collapsed Riemannian manifolds with bounded sectional curvature},
  author={Xiaochun Rong},
In the last two decades, one of the most important developments in Riemannian geometry is the collapsing theory of Cheeger-Fukaya-Gromov. A Riemannian manifold is called (sufficiently) collapsed if its dimension looks smaller than its actual dimension while its sectional curvature remains bounded (say a very thin flat torus looks like a circle in a bared eyes). We will survey the development of collapsing theory and its applications to Riemannian geometry since 1990. The common starting point… 
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