Titlebook: Geometry and Analysis of Fractals; Hong Kong, December De-Jun Feng,Ka-Sing Lau Conference proceedings 2014 Springer-Verlag Berlin Heidelbe

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2194-1009 ments 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..978-3-662-51376-7978-3-662-43920-3Series ISSN 2194-1009 Series E-ISSN 2194-1017

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Mandelbrot Cascades and Related Topics,he Chinese Hong-Kong University. It gathers recent advances in Mandelbrot cascades theory and related topics, namely branching random walks, directed polymers on disordered trees, multifractal analysis, and dynamical systems.

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Quasisymmetric Modification of Metrics on Self-Similar Sets,on a self-similar set being quasisymmetric to each other. As an application, we construct metrics on the Sierpinski carpet which is quasisymmetric with respect to the Euclidean metrics and obtain an upper estimate of the conformal dimension of the Sierpinski carpet.

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The Geometry of Fractal Percolation, goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation. The extensions go in three directions:.. the statements work for all directions, not almost all,.. the statements are true for more general projections, for example ra

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Self-affine Sets and the Continuity of Subadditive Pressure,ns of self-affine sets. De-Jun Feng and the author recently solved a folklore open problem, by proving that the affinity dimension is a continuous function of the defining maps. The proof also yields the continuity of a topological pressure arising in the study of random matrix products. I survey th

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Stability Properties of Fractal Curvatures,rential geometry. In recent years their fractal versions have been introduced via approximation by parallel sets of small distances. In the present paper stability properties of the corresponding limits under small perturbations of these neighborhoods are studied. The well-known Minkowski content ma