Differential and Riemannian geometry

This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics.

The volume consists of a set of surveys on geometry in the broad sense.

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry.

This book consists of contributions from the participants of the Abel Symposium 2019 held in Alesund, Norway.

This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements.

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology.

This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds.

This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras.

This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics.

This volume arose from a semester at CIRM-Luminy on "e;Thermodynamic Formalism: Applications to Probability, Geometry and Fractals"e; which brought together leading experts in the area to discuss topical problems and recent progress.

This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory.

This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems.

This volume originated in talks given in Cortona at the conference "e;Geometric aspects of harmonic analysis"e; held in honor of the 70th birthday of Fulvio Ricci.

This brief focuses on the structural properties of nonlinear time-delay systems.

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.