* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow.

* Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.

In this volume authors of academia and practice provide practitioners, scientists and graduate students with a good overview of basic methods and paradigms, as well as important issues and trends across the broad spectrum of parallel and distributed processing. In particular, the book covers fundamental topics such as efficient parallel algorithms, languages for parallel processing, parallel operating systems, architecture of parallel and distributed systems, management of resources, tools for parallel computing, parallel database systems and multimedia object servers, and networking aspects of distributed and parallel computing. Three chapters are dedicated to applications: parallel and distributed scientific computing, high-performance computing in molecular sciences, and multimedia applications for parallel and distributed systems. Summing up, the Handbook is indispensable for academics and professionals who are interested in learning the leading expert`s view of the topic.

This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space - Time - Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy - Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson-Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

In this volume authors of academia and practice provide practitioners, scientists and graduate students with a good overview of basic methods and paradigms, as well as important issues and trends across the broad spectrum of parallel and distributed processing. In particular, the book covers fundamental topics such as efficient parallel algorithms, languages for parallel processing, parallel operating systems, architecture of parallel and distributed systems, management of resources, tools for parallel computing, parallel database systems and multimedia object servers, and networking aspects of distributed and parallel computing. Three chapters are dedicated to applications: parallel and distributed scientific computing, high-performance computing in molecular sciences, and multimedia applications for parallel and distributed systems. Summing up, the Handbook is indispensable for academics and professionals who are interested in learning the leading experts view of the topic.

* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow.

* Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.