Geometry of Sets and Measures in Euclidean Spaces

Fractals and Rectifiability
Author: Pertti Mattila
Publisher: Cambridge University Press
ISBN: 9780521655958
Category: Mathematics
Page: 343
View: 4342

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This book studies the geometric properties of general sets and measures in euclidean space.

Geometry and Analysis of Fractals

Hong Kong, December 2012
Author: De-Jun Feng,Ka-Sing Lau
Publisher: Springer
ISBN: 3662439204
Category: Mathematics
Page: 358
View: 3230

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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.

Fractured Fractals and Broken Dreams

Self-similar Geometry Through Metric and Measure
Author: Guy David,Stephen W. Semmes,Stephen Semmes,Guy Rene Pierre Pierre
Publisher: Oxford University Press
ISBN: 9780198501664
Category: Mathematics
Page: 212
View: 5190

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This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a "pattern" and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein providea fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. One of the main features of the present text is that the basic framework is completely new. This makes it easier for people to get into the field. There are many open problems, with plenty of opportunities that are likely to be close at hand, particularly as concerns the exploration of examples. Onthe other hand the general framework is quite broad and provides the possibility for future discoveries of some magnitude. Fractual geometries can arise in many different ways mathematically, but there is not so much general language for making comparisons. This book provides some tools for doing this, and a place where researchers in different areas can find common ground and basic information.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics


Author: David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher: American Mathematical Soc.
ISBN: 0821891472
Category: Mathematics
Page: 399
View: 1814

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This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

In the Tradition of Ahlfors-Bers, IV

Ahlfors-Bers Colloquium, May 19-22, 2005, University of Michigan, Ann Arbor, Michigan
Author: Richard Douglas Canary
Publisher: American Mathematical Soc.
ISBN: 0821842277
Category: Mathematics
Page: 229
View: 4052

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The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic manifolds, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields, such as algebraic geometry, mathematical physics, dynamics, geometric group theory, number theory, and topology. The triannual Ahlford-Bers colloquia serve as a venue to disseminate the relevant work to the wider mathematical community and bring the key participants together to ponder future directions in the field. The present volume includes a wide range of articles in the fields central to this legacy. The majority of articles present new results, but there are expository articles as well.

Recent Developments in Fractals and Related Fields

Conference on Fractals and Related Fields III, île de Porquerolles, France, 2015
Author: Julien Barral,Stéphane Seuret
Publisher: Birkhäuser
ISBN: 3319578057
Category: Mathematics
Page: 312
View: 6888

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This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Submanifolds in Carnot Groups


Author: Davide Vittone
Publisher: Edizioni della Normale
ISBN: N.A
Category: Mathematics
Page: 180
View: 9842

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The book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure; particular emphasis is given to the case of Heisenberg groups. A Geometric Measure Theory viewpoint is adopted, and features as intrinsic perimeters, Hausdorff measures, area formulae, calibrations and minimal surfaces are considered. Area formulae for the measure of submanifolds of arbitrary codimension are obtained in Carnot groups. Intrinsically regular hypersurfaces in the Heisenberg group are extensively studied: suitable notions of graphs are introduced, together with area formulae leading to the analysis of Plateau and Bernstein type problems.

Report


Author: N.A
Publisher: N.A
ISBN: 9789513916060
Category: Functional analysis
Page: 64
View: 9950

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