Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable currents are applied, and some important integral-geometric formulas are derived. Moreover, an approach to curvatures for a class of fractals is presented, which uses approximation by the rescaled curvature measures of small neighborhoods. The book collects results published during the last few decades in a nearly comprehensive way.

Global analysis. --- Mathematics. --- Discrete groups. --- Global differential geometry. --- Global Analysis and Analysis on Manifolds. --- Measure and Integration. --- Convex and Discrete Geometry. --- Differential Geometry. --- Set theory. --- Geometry, Differential --- Groups, Discrete --- Discrete mathematics --- Infinite groups --- Math --- Science --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Measure theory. --- Convex geometry . --- Discrete geometry. --- Differential geometry. --- Differential geometry --- Geometry --- Combinatorial geometry --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Over the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its own right. The interplay between fractal geometry, analysis and stochastics has highly influenced recent developments in mathematical modeling of complicated structures. This process has been forced by problems in these areas related to applications in statistical physics, biomathematics and finance. This book is a collection of survey articles covering many of the most recent developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals. The authors were the keynote speakers at the conference "Fractal Geometry and Stochastics IV" at Greifswald in September 2008.

Fractals. --- Stochastic processes. --- Fractals --- Stochastic processes --- Mathematics --- Geometry --- Mathematical Statistics --- Physical Sciences & Mathematics --- Random processes --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Mathematics. --- Geometry. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probabilities --- Dimension theory (Topology) --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Euclid's Elements --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)