Regularity Theory For Mean Curvature Flow
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Regularity Theory For Mean Curvature Flow
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Author : Klaus Ecker
language : en
Publisher:
Release Date : 2004
Regularity Theory For Mean Curvature Flow written by Klaus Ecker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Courbure categories.
This work is 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. A major example is Hamilton's Ricci flow program, which has the aim of settling Thurston's geometrization conjecture, with recent major progress due to Perelman. Another important application of a curvature flow process is the resolution of the famous Penrose conjecture in general relativity by Huisken and Ilmanen. Under mean curvature flow, surfaces usually develop singularities in finite time. This work presents techniques for the study of singularities of mean curvature flow and is largely based on the work of K. Brakke, although more recent developments are incorporated.
Regularity Theory For Mean Curvature Flow
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Author : K. Ecker
language : en
Publisher:
Release Date : 2004
Regularity Theory For Mean Curvature Flow written by K. Ecker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Regularity Theory For Mean Curvature Flow
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Author : Klaus Ecker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Regularity Theory For Mean Curvature Flow written by Klaus Ecker 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 2012-12-06 with Mathematics categories.
* 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.
Brakke S Mean Curvature Flow
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Author : Yoshihiro Tonegawa
language : en
Publisher: Springer
Release Date : 2019-04-09
Brakke S Mean Curvature Flow written by Yoshihiro Tonegawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-09 with Mathematics categories.
This book explains the notion of Brakke’s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory. The focus of study is a time-parameterized family of k-dimensional surfaces in the n-dimensional Euclidean space (1 ≤ k in
Elliptic Regularization And Partial Regularity For Motion By Mean Curvature
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Author : Tom Ilmanen
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Elliptic Regularization And Partial Regularity For Motion By Mean Curvature written by Tom Ilmanen 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 1994 with Mathematics categories.
We study Brakke's motion of varifolds by mean curvature in the special case that the initial surface is an integral cycle, giving a new existence proof by mean of elliptic regularization. Under a uniqueness hypothesis, we obtain a weakly continuous family of currents solving Brakke's motion. These currents remain within the corresponding level-set motion by mean curvature, as defined by Evans-Spruck and Chen-Giga-Goto. Now let [italic capital]T0 be the reduced boundary of a bounded set of finite perimeter in [italic capital]R[superscript italic]n. If the level-set motion of the support of [italic capital]T0 does not develop positive Lebesgue measure, then there corresponds a unique integral [italic]n-current [italic capital]T, [partial derivative/boundary/degree of a polynomial symbol][italic capital]T = [italic capital]T0, whose time-slices form a unit density Brakke motion. Using Brakke's regularity theorem, spt [italic capital]T is smooth [script capital]H[superscript italic]n-almost everywhere. In consequence, almost every level-set of the level-set flow is smooth [script capital]H[superscript italic]n-almost everywhere in space-time.
Topics In Modern Regularity Theory
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Author : Giuseppe Mingione
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-26
Topics In Modern Regularity Theory written by Giuseppe Mingione 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 2012-04-26 with Mathematics categories.
This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010. The contributors, Nicola Fusco, Tristan Rivière and Reiner Schätzle, provide three updated and extensive introductions to various aspects of modern Regularity Theory concerning: mathematical modelling of thin films and related free discontinuity problems, analysis of conformally invariant variational problems via conservation laws, and the analysis of the Willmore functional. Each contribution begins with a very comprehensive introduction, and is aimed to take the reader from the introductory aspects of the subject to the most recent developments of the theory.
Mean Curvature Flow
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Author : Theodora Bourni
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-12-07
Mean Curvature Flow written by Theodora Bourni and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-07 with Mathematics categories.
With contributions by leading experts in geometric analysis, this volume is documenting the material presented in the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, on May 29 - June 1, 2018. The central topic of the 2018 lectures was mean curvature flow, and the material in this volume covers all recent developments in this vibrant area that combines partial differential equations with differential geometry.
Mean Curvature Flow And Isoperimetric Inequalities
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Author : Manuel Ritoré
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-01
Mean Curvature Flow And Isoperimetric Inequalities written by Manuel Ritoré 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 2010-01-01 with Mathematics categories.
Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Minimal Surfaces Integrable Systems And Visualisation
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Author : Tim Hoffmann
language : en
Publisher: Springer Nature
Release Date : 2021-05-06
Minimal Surfaces Integrable Systems And Visualisation written by Tim Hoffmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.
This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and Leicester between 2016 and 2019. Within the theme of the network, the presented articles cover a broad range of topics and explore exciting links between problems related to the mean curvature of surfaces in homogeneous 3-manifolds, like minimal surfaces, CMC surfaces and mean curvature flows, integrable systems and visualisation. Combining research and overview articles by prominent international researchers, the book offers a valuable resource for both researchers and students who are interested in this research area.
Lecture Notes On Mean Curvature Flow Barriers And Singular Perturbations
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Author : Giovanni Bellettini
language : en
Publisher: Springer
Release Date : 2014-05-13
Lecture Notes On Mean Curvature Flow Barriers And Singular Perturbations written by Giovanni Bellettini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-13 with Mathematics categories.
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.