Geometric Analysis Around Scalar Curvatures PDF Download
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| Author | : Fei Han |
| Publisher | : World Scientific |
| Total Pages | : 221 |
| Release | : 2016-04-18 |
| Genre | : Mathematics |
| ISBN | : 9813100567 |
Download Geometric Analysis Around Scalar Curvatures Book in PDF, ePub and Kindle
This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations.
| Author | : Dan A. Lee |
| Publisher | : American Mathematical Society |
| Total Pages | : 377 |
| Release | : 2021-12-20 |
| Genre | : Mathematics |
| ISBN | : 1470466236 |
Download Geometric Relativity Book in PDF, ePub and Kindle
Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the first time these topics have been gathered into a single place and presented with an advanced graduate student audience in mind; several dozen exercises are also included. The main prerequisite for this book is a working understanding of Riemannian geometry and basic knowledge of elliptic linear partial differential equations, with only minimal prior knowledge of physics required. The second part of the book includes a short crash course on general relativity, which provides background for the study of asymptotically flat initial data sets satisfying the dominant energy condition.
| Author | : Sirakov Boyan |
| Publisher | : World Scientific |
| Total Pages | : 5396 |
| Release | : 2019-02-27 |
| Genre | : Mathematics |
| ISBN | : 9813272899 |
Download Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) Book in PDF, ePub and Kindle
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
| Author | : Richard Wentworth |
| Publisher | : World Scientific |
| Total Pages | : 412 |
| Release | : 2018-06-28 |
| Genre | : Mathematics |
| ISBN | : 9813229101 |
Download The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles Book in PDF, ePub and Kindle
In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.
| Author | : Iva Stavrov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 243 |
| Release | : 2020-11-12 |
| Genre | : Education |
| ISBN | : 1470456281 |
Download Curvature of Space and Time, with an Introduction to Geometric Analysis Book in PDF, ePub and Kindle
This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.
| Author | : Luigi Accardi |
| Publisher | : World Scientific |
| Total Pages | : 243 |
| Release | : 2017-08-29 |
| Genre | : Mathematics |
| ISBN | : 9813225475 |
Download White Noise Analysis And Quantum Information Book in PDF, ePub and Kindle
This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. These fields are rather wide and are of a strongly interdisciplinary nature. For such a purpose, we strove to bridge among these interdisciplinary fields in our Workshop on IDAQP and their Applications that was held at the Institute for Mathematical Sciences, National University of Singapore from 3-7 March 2014. Readers will find that this volume contains all the exciting contributions by well-known researchers in search of new directions in these fields.
| Author | : Owen Dearricott |
| Publisher | : Cambridge University Press |
| Total Pages | : 402 |
| Release | : 2020-10-22 |
| Genre | : Mathematics |
| ISBN | : 1108879993 |
Download Differential Geometry in the Large Book in PDF, ePub and Kindle
The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry.
| Author | : Mikhael Gromov |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2023 |
| Genre | : Curvature |
| ISBN | : 9789811249990 |
Download Perspectives in Scalar Curvature Book in PDF, ePub and Kindle
"Volume I contains a long article by Misha Gromov based on his many years of involvement in this subject. It came from lectures delivered in Spring 2019 at IHES. There is some background given. Many topics in the field are presented, and many open problems are discussed. One intriguing point here is the crucial role played by two seemingly unrelated analytic means: index theory of Dirac operators and geometric measure theory. Very recently there have been some real breakthroughs in the field. Volume I has several survey articles written by people who were responsible for these results. For Volume II, many people in areas of mathematics and physics, whose work is somehow related to scalar curvature, were asked to write about this in any way thay pleased. This gives rise to a wonderful collection of articles, some with very broad and historical views, others which discussed specific fascinating subjects. These two books give a rich and powerful view of one of geometry's very appealing sides"--
| Author | : Elaine Chew |
| Publisher | : World Scientific |
| Total Pages | : 315 |
| Release | : 2016-07-21 |
| Genre | : Mathematics |
| ISBN | : 9813140119 |
Download Mathemusical Conversations: Mathematics And Computation In Music Performance And Composition Book in PDF, ePub and Kindle
Mathemusical Conversations celebrates the understanding of music through mathematics, and the appreciation of mathematics through music. This volume is a compilation of the invited talks given at the Mathemusical Conversations workshop that took place in Singapore from 13-15 February 2015, organized by Elaine Chew in partnership with Gérard Assayag for the scientific program and with Bernard Lanskey for the artistic program. The contributors are world experts and leading scholars, writing on the intersection of music and mathematics. They also focus on performance and composition, two topics which are foundational both to the understanding of human creativity and to the creation of tomorrow's music technologies. This book is essential reading for researchers in both music and mathematics. It will also appeal more broadly to scholars, students, musicians, and anyone interested in new perspectives on the intimate relationship between these two universal human activities.
| Author | : Weizhu Bao |
| Publisher | : World Scientific |
| Total Pages | : 243 |
| Release | : 2023-01-17 |
| Genre | : Mathematics |
| ISBN | : 9811266158 |
Download Modeling And Simulation For Collective Dynamics Book in PDF, ePub and Kindle
The thematic program Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications was held at the Institute for Mathematical Sciences at the National University of Singapore, from September 2019 to March 2020. Leading experts presented tutorials and special lectures geared towards the participating graduate students and junior researchers.Readers will find in this significant volume four expanded lecture notes with self-contained tutorials on modeling and simulation for collective dynamics including individual and population approaches for population dynamics in mathematical biology, collective behaviors for Lohe type aggregation models, mean-field particle swarm optimization, and consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints.This volume serves to inspire graduate students and researchers who will embark into original research work in kinetic models for collective dynamics and their applications.
