Differential and Riemannian geometry

This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future.

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.

The Taniguchi Symposium on global analysis on manifolds focused mainly on the relationships between some geometric structures of manifolds and analysis, especially spectral analysis on noncompact manifolds.

The implicit function theorem is part of the bedrock of mathematical analysis and geometry.

The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold.

Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups.

Complex Finsler metrics appear naturally in complex analysis.

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.

In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J.

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

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.

Mathematical Visualization is a young new discipline.

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics.

This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022.

This book explains and helps readers to develop geometric intuition as it relates to differential forms.

This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point.

The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields.

In view of the significance of the array manifold in array processing and array communications, the role of differential geometry as an analytical tool cannot be overemphasized.

This classic work is now available in an unabridged paperback edition.

Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A.

The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics.

Metric and Differential Geometry grew out of a similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing.

The papers collected in this volume are contributions to the 43rd session of the Seminaire ' de mathematiques ' superieures ' (SMS) on "e;Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.

The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length.

With each methodology treated in its own chapter, this monograph is a thorough exploration of several theories that can be used to find explicit formulas for heat kernels for both elliptic and sub-elliptic operators.

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

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

Historical interest and studies of Weyl's role in the interplay between 20th-century mathematics, physics and philosophy have been increasing since the middle 1980s, triggered by different activities at the occasion of the centenary of his birth in 1985, and are far from being exhausted.

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems.

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.

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.

Noncommutative differential geometry is a new approach to classical geometry.

These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.

The 2nd edition of this textbook features more than 100 pages of new material, including four new chapters, as well as an improved discussion of differential geometry concepts and their applications.

This book presents properties, examples, rigidity theorems and classification results of such Finsler metrics.

This book, first published in 2006, details how limit processes can be represented algebraically.

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory.