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The differential structure of metric measure space

理科
2016-03-28
1 39 0 0
摘要:In the past ten years, the metric measure spaces with Ricci curvature bound which was proposed by Lott-Sturm-Villani, was studied by researcher from many different areas. In this talk I will introduce some recent results on the differential structure of metric measure spaces, including the non-smooth Sobolev space, Barky- Emery theory, and the notion of tangent/cotangent modules in non-smooth framework. On the metric measure spaces with curvature-dimension condition RCD (K;N), we obtainan improved Bochner inequality and propose a de nition of N-dimensional Ricci tensor.
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