On the geometry of metric measure spaces. II
Citations
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Cites methods from "On the geometry of metric measure s..."
...After the writing of the paper was essentially completed we learned of related work by Karl-Theodor Sturm [41, 42 ]....
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Cites background from "On the geometry of metric measure s..."
...This gave rise to a wide theory of analysis in metric measure spaces, where this convexity property was chosen as a definition for the curvature bounds (see [219, 288, 289])....
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Cites background from "On the geometry of metric measure s..."
...on Ricf = λgfor some constant λis exactly the gradient Ricci soliton equation, which plays an important role in the theory of Ricci flow. Moreover Ricf has a natural extension to metric measure spaces [21, 35, 36]. When fis a constant function, the Bakry-Emery Ricci tensor is the Ricci tensor so it is natural to investigate what geometric and topological results for the Ricci tensor extend to the Bakry-Emery R...
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References
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"On the geometry of metric measure s..." refers methods in this paper
...For proofs and further details we refer to [ BH99 ], [Gr99], and [BBI01]....
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"On the geometry of metric measure s..." refers background or methods in this paper
...For further reading we recommend [16], [29], [45], [55] and [56]....
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...Villani [55] which gives an excellent survey on the whole field....
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...[55]....
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...(i), (ii) See [45], [55]....
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"On the geometry of metric measure s..." refers background in this paper
...Perelman [43] in the context of his work on the geometrization conjecture for 3-manifolds....
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Additional excerpts
...[36], [10], [14] and [47]....
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"On the geometry of metric measure s..." refers background in this paper
...For proofs and further details we refer to [7], [22], and [8]....
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...We summarize some of the basic properties of these metric spaces and refer to [9], [22], [8] and [44] for further details....
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