Maximum Principles And Geometric Applications
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Maximum Principles And Geometric Applications
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Author : Luis J. Alías
language : en
Publisher: Springer
Release Date : 2016-02-13
Maximum Principles And Geometric Applications written by Luis J. Alías and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-13 with Mathematics categories.
This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter. In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on. Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.
Maximum Principles On Riemannian Manifolds And Applications
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Author : Stefano Pigola
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Maximum Principles On Riemannian Manifolds And Applications written by Stefano Pigola 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.
Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
The Fractional Laplacian
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Author : Wenxiong Chen
language : en
Publisher: World Scientific
Release Date : 2020-06-09
The Fractional Laplacian written by Wenxiong Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-09 with Mathematics categories.
This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.
Control Theory From The Geometric Viewpoint
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Author : Andrei A. Agrachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-15
Control Theory From The Geometric Viewpoint written by Andrei A. Agrachev 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 2004-04-15 with Language Arts & Disciplines categories.
This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.
Ricci Flow And Geometric Applications
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Author : Michel Boileau
language : en
Publisher: Springer
Release Date : 2016-09-09
Ricci Flow And Geometric Applications written by Michel Boileau and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-09 with Mathematics categories.
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.
Contemporary Research In Elliptic Pdes And Related Topics
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Author : Serena Dipierro
language : en
Publisher: Springer
Release Date : 2019-07-12
Contemporary Research In Elliptic Pdes And Related Topics written by Serena Dipierro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Mathematics categories.
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Differential Geometric Structures And Applications
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Author : Vladimir Rovenski
language : en
Publisher: Springer Nature
Release Date : 2024-03-15
Differential Geometric Structures And Applications written by Vladimir Rovenski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-15 with Mathematics categories.
This proceedings contains a collection of selected, peer-reviewed contributions from the 4th International Workshop "Differential Geometric Structures and Applications" held in Haifa, Israel from May 10–13, 2023. The papers included in this volume showcase the latest advancements in modern geometry and interdisciplinary applications in fields ranging from mathematical physics to biology. Since 2008, this workshop series has provided a platform for researchers in pure and applied mathematics, including students, to engage in discussions and explore the frontiers of modern geometry. Previous workshops in the series have focused on topics such as "Reconstruction of Geometrical Objects Using Symbolic Computations" (2008), "Geometry and Symbolic Computations" (2013), and "Geometric Structures and Interdisciplinary Applications" (2018).
Recent Advances In Pure And Applied Mathematics
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Author : Francisco Ortegón Gallego
language : en
Publisher: Springer Nature
Release Date : 2020-04-11
Recent Advances In Pure And Applied Mathematics written by Francisco Ortegón Gallego and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-11 with Mathematics categories.
This volume comprises high-quality works in pure and applied mathematics from the mathematical communities in Spain and Brazil. A wide range of subjects are covered, ranging from abstract algebra, including Lie algebras, commutative semigroups, and differential geometry, to optimization and control in real world problems such as fluid mechanics, the numerical simulation of cancer PDE models, and the stability of certain dynamical systems. The book is based on contributions presented at the Second Joint Meeting Spain-Brazil in Mathematics, held in Cádiz in December 2018, which brought together more than 330 delegates from around the world. All works were subjected to a blind peer review process. The book offers an excellent summary of the recent activity of Spanish and Brazilian research groups and will be of interest to researchers, PhD students, and graduate scholars seeking up-to-date knowledge on these pure and applied mathematics subjects.
Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds
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Author : Bruno Bianchini
language : en
Publisher: Springer Nature
Release Date : 2021-01-18
Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds written by Bruno Bianchini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.
This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Lorentzian Geometry And Related Topics
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Author : María A. Cañadas-Pinedo
language : en
Publisher: Springer
Release Date : 2018-03-06
Lorentzian Geometry And Related Topics written by María A. Cañadas-Pinedo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Mathematics categories.
This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.