Differential and Riemannian geometry

This book collects papers presented in the Invited Workshop, "e;Liutex and Third Generation of Vortex Definition and Identification for Turbulence,"e; from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference.

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry.

This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc.

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common?

This book collects original peer-reviewed contributions to the conferences organised by the international research network "e;Minimal surfaces: Integrable Systems and Visualization"e; financed by the Leverhulme Trust.

This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics.

This book is an outgrowth of the conference "e;Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods"e; that was held in Paris in May 2016.

This volume presents lectures given at the Wisla 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them.

This book focuses on a selection of special topics, with emphasis on past and present research of the authors on "e;canonical"e; Riemannian metrics on smooth manifolds.

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the study of scalar curvature rigidity and positive mass theorems using spinors and the Dirac operator It is intended for both graduate students and researchers.

This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces.

This book presents a multidisciplinary guide to gauge theory and gravity, with chapters by the world's leading theoretical physicists, mathematicians, historians and philosophers of science.

This concise and practical textbook presents the essence of the theory on smooth manifolds.

This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July 2019.

This book describes analytical methods for modelling drop evaporation, providing the mathematical tools needed in order to generalise transport and constitutive equations and to find analytical solutions in curvilinear coordinate systems.

This book opens with an axiomatic description of Euclidean and non-Euclidean geometries.

This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics.

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing.

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing.

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics.

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory.

This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis.

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries.

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2).

This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects.

This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute.

This book aims to provide a friendly introduction to non-commutative geometry.

This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe.

This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications.

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds.

This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday.

This updated and expanded edition presents a highly accurate specification for part surface machining.

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical.

This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees.

The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces.

This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures, an essential tool in the study of pseudo-Riemannian homogeneous spaces.

This volume presents lectures given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

This textbook provides a coherent, integrated look at various topics from undergraduate analysis.

This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry.

This book explains the foundations of holomorphic curve theory in contact geometry.

This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics.

Aimed toward graduate students and research mathematicians, with minimal prerequisites this book  provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory.

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained.

This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry.

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 - February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics.

This volume resulted from presentations given at the international "e;Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series"e;, that took place at the Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain.

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.

This book consists of two lecture notes on geometric flow equations (O.

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical.