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Ricci Curvature Comparison

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Part of the Graduate Texts in Mathematics book series (GTM,volume 171 )

Abstract

In this chapter we prove some of the fundamental results for manifolds with lower Ricci curvature bounds. Two important techniques will be developed: Relative volume comparison and weak upper bounds for the Laplacian of distance functions. Later some of the analytic estimates we develop here will be used to estimate Betti numbers for manifolds with lower curvature bounds.

Keywords

  • Nonnegative Ricci Curvature
  • Relative Volume Comparison
  • Betti Number Estimate
  • Ricci-flat Metrics
  • Decreasing Distance Function

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  • DOI: 10.1007/978-3-319-26654-1_7
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Petersen, P. (2016). Ricci Curvature Comparison. In: Riemannian Geometry. Graduate Texts in Mathematics, vol 171 . Springer, Cham. https://doi.org/10.1007/978-3-319-26654-1_7

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