Geometric Evolution Equations
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Geometric Evolution Equations
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Author : Shu-Cheng Chang
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Geometric Evolution Equations written by Shu-Cheng Chang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The Workshop on Geometric Evolution Equations was a gathering of experts that produced this comprehensive collection of articles. Many of the papers relate to the Ricci flow and Hamilton's program for understanding the geometry and topology of 3-manifolds. The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solution of Thurston's Geometrization Conjecture and the Poincare Conjecture. Yet applying the method poses serious technical problems. Contributors to this volume explain some of these issues and demonstrate a noteworthy deftness in the handling of technical areas. Various topics in geometric evolution equations and related fields are presented. Among other topics covered are minimal surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kahler-Ricci flow, function theory on Kahler manifolds, flows of plane curves, convexity estimates, and the Christoffel-Minkowski problem. The material is suitable for graduate students and researchers interested in geometric analysis and connections to topology. Related titles of interest include The Ricci Flow: An Introduction.
Geometric Evolution Equations
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Author : Stacey E. Chastain
language : en
Publisher:
Release Date : 2000
Geometric Evolution Equations written by Stacey E. Chastain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Geometric Curve Evolution And Image Processing
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Author : Frédéric Cao
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-02-27
Geometric Curve Evolution And Image Processing written by Frédéric Cao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-27 with Mathematics categories.
In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.
Fourth Order Geometric Evolution Equations
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Author : Glen Edward Wheeler
language : en
Publisher:
Release Date : 2009
Fourth Order Geometric Evolution Equations written by Glen Edward Wheeler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Calculus of variations categories.
Surface Evolution Equations
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Author : Yoshikazu Giga
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Surface Evolution Equations written by Yoshikazu Giga and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions.
Calculus Of Variations And Geometric Evolution Problems
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Author : F. Bethuel
language : en
Publisher: Springer
Release Date : 2006-11-14
Calculus Of Variations And Geometric Evolution Problems written by F. Bethuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.
Geometric Evolution Equations And P Harmonic Theory With Applications In Differential Geometry
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Author : Junfang Li
language : en
Publisher:
Release Date : 2006
Geometric Evolution Equations And P Harmonic Theory With Applications In Differential Geometry written by Junfang Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations, Partial categories.
Evolution Equations
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Author : David Ellwood
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-26
Evolution Equations written by David Ellwood and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-26 with Mathematics categories.
This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Moving Interfaces And Quasilinear Parabolic Evolution Equations
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Author : Jan Prüss
language : en
Publisher: Birkhäuser
Release Date : 2016-07-25
Moving Interfaces And Quasilinear Parabolic Evolution Equations written by Jan Prüss and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
Stability Analysis Of Geometric Evolution Equations With Triple Lines And Boundary Contact
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Author : Daniel Depner
language : en
Publisher:
Release Date : 2010
Stability Analysis Of Geometric Evolution Equations With Triple Lines And Boundary Contact written by Daniel Depner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.