Analysis and Geometry of Metric Measure Spaces: Lecture Notes of the 50th Seminaire De Mathematiques Superieures (SMS), Montreal, 2011

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American Mathematical Soc., 2013 - Mathematics - 220 pages
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This book contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieures in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation. In recent decades, metric measure spaces have emerged as a fruitful source of mathematical questions in their own right, and as indispensable tools for addressing classical problems in geometry, topology, dynamical systems, and partial differential equations. The summer school was designed to lead young scientists to the research frontier concerning the analysis and geometry of metric measure spaces, by exposing them to a series of minicourses featuring leading researchers who highlighted both the state-of-the-art and some of the exciting challenges which remain. This volume attempts to capture the excitement of the summer school itself, presenting the reader with glimpses into this active area of research and its connections with other branches of contemporary mathematics.
 

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Contents

Analysis on the Sierpinski Carpet
27
Heat Kernel Estimates SobolevType Inequalities and Riesz Transform
55
Lectures on MaTrudingerWang Curvature and Regularity of Optimal
119
Geometry Regularity
142
A Proof of Bobkovs Spectral Bound For Convex Domains via Gaussian Fitting
181
A Visual Introduction to Riemannian Curvatures and Some Discrete
197
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