The Hodge Laplacian
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Analysis Of The Hodge Laplacian On The Heisenberg Group
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Author : Detlef Muller
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Analysis Of The Hodge Laplacian On The Heisenberg Group written by Detlef Muller 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 2014-12-20 with Mathematics categories.
The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1
The Hodge Laplacian written by Dorina Mitrea 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 2016-10-10 with Mathematics categories.
The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains. Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents: Preface Introduction and Statement of Main Results Geometric Concepts and Tools Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism Additional Results and Applications Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis Bibliography Index
Layer Potentials The Hodge Laplacian And Global Boundary Problems In Nonsmooth Riemannian Manifolds written by Dorina Mitrea 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 2001 with Boundary value problems categories.
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds. In the first part (ss1-4), we develop a theory for Cauchy type operators on Lipschitz submanifolds of co dimension one (focused on boundedness properties and jump relations) and solve the $Lp$-Dirichlet problem, with $p$ close to $2$, for general second-order strongly elliptic systems. The solution is represented in the form of layer potentials and optimal non tangential maximal function estimates are established.This analysis is carried out under smoothness assumptions (for the coefficients of the operator, metric tensor and the underlying domain) which are in the nature of best possible. In the second part of the monograph, ss5-13, we further specialize this discussion to the case of Hodge Laplacian $\Delta: =-d\delta-\delta d$. This time, the goal is to identify all (pairs of) natural boundary conditions of Neumann type. Owing to the structural richness of the higher degree case we are considering, the theory developed here encompasses in a unitary fashion many basic PDE's of mathematical physics. Its scope extends to also cover Maxwell's equations, dealt with separately in s14. The main tools are those of PDE's and harmonic analysis, occasionally supplemented with some basic facts from algebraic topology and differential geometry.
On The Lp Spectrum Of The Hodge Laplacian And Logarithmic Sobolev Inequalities On Non Compact Manifolds written by Nelia Sofocli Charalambous 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.
The Heat Kernel Weighted Hodge Laplacian On Noncompact Manifolds written by Edward Lee Bueler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
The Laplacian On A Riemannian Manifold written by Steven Rosenberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-09 with Mathematics categories.
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
The Hodge Laplacian written by Dorina Mitrea 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 2016-10-10 with Mathematics categories.
The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains. Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents: Preface Introduction and Statement of Main Results Geometric Concepts and Tools Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism Additional Results and Applications Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis Bibliography Index
Geometry Of The Laplace Operator written by Robert Osserman 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 1980 with Mathematics categories.
The Hypoelliptic Laplacian And Ray Singer Metrics Am 167 written by Jean-Michel Bismut and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-18 with Mathematics categories.
This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained. The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.
Quantum Field Theory Iii Gauge Theory written by Eberhard Zeidler 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 2011-08-17 with Mathematics categories.
In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
The Hodge Laplacian
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Author : Dorina Mitrea
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-10-10
Layer Potentials The Hodge Laplacian And Global Boundary Problems In Nonsmooth Riemannian Manifolds
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Author : Dorina Mitrea
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
On The Lp Spectrum Of The Hodge Laplacian And Logarithmic Sobolev Inequalities On Non Compact Manifolds
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Author : Nelia Sofocli Charalambous
language : en
Publisher:
Release Date : 2004
The Heat Kernel Weighted Hodge Laplacian On Noncompact Manifolds
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Author : Edward Lee Bueler
language : en
Publisher:
Release Date : 1997
The Laplacian On A Riemannian Manifold
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Author : Steven Rosenberg
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-09
The Hodge Laplacian
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Author : Dorina Mitrea
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-10-10
Geometry Of The Laplace Operator
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Author : Robert Osserman
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
The Hypoelliptic Laplacian And Ray Singer Metrics Am 167
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Author : Jean-Michel Bismut
language : en
Publisher: Princeton University Press
Release Date : 2008-08-18
Quantum Field Theory Iii Gauge Theory
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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-17