Geometry and Analysis of Fractals: Hong Kong, December 2012 (Springer Proceedings in Mathematics & Statistics Book 88)

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. Front Matter....Pages i-viii Mandelbrot Cascades and Related Topics....Pages 1-45 Law of Pure Types and Some Exotic Spectra of Fractal Spectral Measures....Pages 47-64 The Role of Transfer Operators and Shifts in the Study of Fractals: Encoding-Models, Analysis and Geometry, Commutative and Non-commutative....Pages 65-95 Generalized Energy Inequalities and Higher Multifractal Moments....Pages 97-113 Some Aspects of Multifractal Analysis....Pages 115-145 Heat Kernels on Metric Measure Spaces....Pages 147-207 Stochastic Completeness of Jump Processes on Metric Measure Spaces....Pages 209-224 Self Similar Sets, Entropy and Additive Combinatorics....Pages 225-252 Quasisymmetric Modification of Metrics on Self-Similar Sets....Pages 253-282 Recent Progress on Dimensions of Projections....Pages 283-301 The Geometry of Fractal Percolation....Pages 303-323 Self-affine Sets and the Continuity of Subadditive Pressure....Pages 325-342 Stability Properties of Fractal Curvatures....Pages 343-354 Back Matter....Pages 355-358