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<title><string language="fre"><![CDATA[Thomas Richard - Lower bounds on Ricci curvature, with a glimpse on limit spaces (Part 4)]]></string></title>
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<string language="fre"><![CDATA[The
goal of these lectures is to introduce some fundamental tools in the 
study of manifolds with a lower bound on Ricci curvature. We will first 
state and prove the laplacian comparison theorem for manifolds with a 
lower bound on the Ricci curvature, and derive some important 
consequences : Bishop-Gromov inequality, Myers theorem, Cheeger-Gromoll 
splitting theorem. Then we will define the Gromov-Hausdorff distance 
between metric spaces which will allow us to consider limits of 
sequences of Riemannian manifolds, along the way we will prove Gromov’s 
precompactness theorem for sequences of manifolds with a Ricci lower 
bound. We will also see on examples what type of degeneration can occur 
when considering these « Ricci limit spaces », we will in particular 
encounter curvature blow up and volume collapsing. One of the major 
point in the study of these limit spaces is to understand which results 
on smooth manifolds with a Ricci lower bound carry on to the limit 
spaces, we will give an introduction to this topic by outlining the 
proof by Cheeger and Colding of the splitting theorem for limit spaces.]]></string></description>
<keyword><string language="fre"><![CDATA[mathématiques]]></string></keyword><keyword><string language="fre"><![CDATA[Grenoble]]></string></keyword><keyword><string language="fre"><![CDATA[école d'été]]></string></keyword><keyword><string language="fre"><![CDATA[institut fourier]]></string></keyword><keyword><string language="fre"><![CDATA[summer school]]></string></keyword><keyword><string language="fre"><![CDATA[geometric analysis]]></string></keyword><keyword><string language="fre"><![CDATA[metric geometry]]></string></keyword><keyword><string language="fre"><![CDATA[topology]]></string></keyword>
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<date><dateTime>2016-06-15</dateTime></date>
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<date><dateTime>2016-06-15</dateTime></date>
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<date><dateTime>2016-06-15</dateTime></date>
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