# Collapsed Riemannian manifolds with bounded sectional curvature

@inproceedings{Rong2003CollapsedRM, title={Collapsed Riemannian manifolds with bounded sectional curvature}, author={Xiaochun Rong}, year={2003} }

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…

#### 3 Citations

How Riemannian Manifolds Converge: A Survey

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How Riemannian Manifolds Converge

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This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometric and topological…

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