Differential and Riemannian geometry

These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986.

The group of Hamiltonian diffeomorphisms Ham(M, 0) of a symplectic mani- fold (M, 0) plays a fundamental role both in geometry and classical mechanics.

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.

This book is based upon my monograph Index Theory for Hamiltonian Systems with Applications published in 1993 in Chinese, and my notes for lectures and courses given at Nankai University, Brigham Young University, ICTP-Trieste, and the Institute of Mathematics of Academia Sinica during the last ten years.

Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic.

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The discoveries of the past decade have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology.

This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows.

In July 1998, I received an e-mail from Alfred Gray, telling me: "e; .

How I have (re-)written this book The book the reader has in hand was supposed to be a new edition of [14].

Foliations, groups and pseudogroups are objects which are closely related via the notion of holonomy.

Boundary problems constitute an essential field of common mathematical interest.

The seminar Symplectic Geometry at the University of Berne in summer 1992 showed that the topic of this book is a very active field, where many different branches of mathematics come tog9ther: differential geometry, topology, partial differential equations, variational calculus, and complex analysis.

This book provides an introduction to topology, differential topology, and differential geometry.

This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds.

In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry.

The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990.

Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H.

The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem.

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

The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology.

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Geometric flows have many applications in physics and geometry.

Filtering is the science of nding the law of a process given a partial observation of it.

Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics.

This book provides a comprehensive introduction to the Calculus of Variations and its use in modelling mechanics and physics problems.

This new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics.

This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance.

This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta.

This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Cordoba, Spain, on February 1-5, 2021.

This book provides an introduction to deformation quantization and its relation to quantum field theory, with a focus on the constructions of Kontsevich and Cattaneo & Felder.

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 volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field.

This volume collects papers based on talks given at the conference "e;Geometrias'19: Polyhedra and Beyond"e;, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal.

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.

This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis-Kapustin (GCK) type.

This book combines the classical and contemporary approaches to differential geometry.

This monograph explores classical electrodynamics from a geometrical perspective with a clear visual presentation throughout.

This book provides an introduction to geometric invariant theory from a differential geometric viewpoint.

This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces.