Geometry and Analysis of Fractals: Hong Kong, December 2012

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De-Jun Feng, Ka-Sing Lau
Springer, Aug 1, 2014 - Mathematics - 358 pages

This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.

 

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Contents

1 Mandelbrot Cascades and Related Topics
1
2 Law of Pure Types and Some Exotic Spectra of Fractal Spectral Measures
47
EncodingModels Analysis and Geometry Commutative and Noncommutative
65
4 Generalized Energy Inequalities and Higher Multifractal Moments
96
5 Some Aspects of Multifractal Analysis
115
6 Heat Kernels on Metric Measure Spaces
146
7 Stochastic Completeness of Jump Processes on Metric Measure Spaces
209
8 Self Similar Sets Entropy and Additive Combinatorics
225
9 Quasisymmetric Modification of Metrics on SelfSimilar Sets
253
10 Recent Progress on Dimensions of Projections
283
11 The Geometry of Fractal Percolation
302
12 Selfaffine Sets and the Continuity of Subadditive Pressure
325
13 Stability Properties of Fractal Curvatures
343
Participants
355
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