The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces

The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces

Paperback (31 Jan 2024)

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Publisher's Synopsis

Equipped with the L2,q-distortion distance ��2,q, the space ��2,q of all metric measure spaces (X, d, ��) 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 ��2,q are presented.

Book information

ISBN: 9781470466961
Publisher: American Mathematical Society
Imprint: American Mathematical Society
Pub date:
Language: English
Number of pages: 111
Weight: 272g
Height: 254mm
Width: 178mm