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The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces by Karl-Theodor Sturm 9781470466961
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The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces by Karl-Theodor Sturm 9781470466961

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Equipped with the L2,q-distortion distance 𝚫2,q, the space 𝕏2,q of all metric measure spaces (X, ｄ, 𝔪) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on ̅𝕏2,q are presented.

Book Information
ISBN 9781470466961
Author Karl-Theodor Sturm
Format Paperback
Page Count 111
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 272g

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