A Treatise on the Differential Geometry of Curves and Surfaces
by Luther Pfahler Eisenhart
The Monge-Ampere equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampere type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis - covering lemmas and set decompositions.
Nonstandard Analysis in Practice (Universitext)
This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks on teaching with infinitesimals.
Geometric Methods in PDE's (Springer INdAM, #13)
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday...
The main purpose of this thesis is to extend methods and results of geometric measure theory to the geometries of sub-riemannian groups. Typical features of sub-riemannian structures historically appeared in several fields of mathematics. Perhaps, the first seeds can be found in the 1909 work by Caratheodory on the second principle of thermodynamics. The Caratheodory theorem can be generalized to distributions of any codimension, whose Lie algebra generates the tangent space at each point. The c...
Exam Board: Edexcel Level: GCSE Subject: Maths First Teaching: September 2015; First Exams: June 2017 Suitable for the 2020 exams Revise tricky topics in a snap Collins Snap Revision helps you focus on the areas of your revision that you find tricky or need extra practice in. Spaced practice opportunities allow you to test, revisit and review your unders...
Radiolaria (Swiss Journal of Geosciences Supplement, #2)
Radiolaria are a very diverse marine siliceous microplankton group that have existed at least snice the Cambrian to the recent. This volume gives a representative view of research topics discussed at the 10th International Meeting of Radiolarian Palaeontologists. The articles of this volume cover mainly radiolarian biochronology and radiolarian fauna changes.
This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providing an integrated presentation fully acc...
This book offers readers a taste of the "unreasonable effectiveness" of Morse theory. It covers many of the most important topics in Morse theory along with applications. The book details topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. In addition, many examples, problems, and illustrations further enhance the value of this useful introduction to Morse Theory.
Regularity of Minimal Surfaces (Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover))
Vorlesungen UEber Asymptotische Reihen (Lecture Notes in Mathematics, #301)
by F Pittnauer
Hamiltonian Structures and Generating Families (Universitext)
by Sergio Benenti
Surveys in Differential Geometry
This volume contains a range of surveys in differential geometry. It includes a photograph section and articles by Michael Atiyah, Egbert Brieskorn, Ciro Ciliberto, Gerard van der Geer, Ralph Cohen, Ernesto Lupercio, Graeme Segal, Simon Donaldson, Daniel Freed, Dorian Goldfeld, Shouwu Zhang, Victor Guillemin, C. Zara, F. Reese Harvey, H. Blaine Lawson Jr., Frederich Hirzebruch, Nigel Hitchen, Dick Kadison, Peter Li, Bong Lian, Kefeng Liu, S.T. Yau, Yu I. Manin, Roger Penrose, Wilfried Schmid, Ka...
The Hodge-Laplacian (De Gruyter Studies in Mathematics, #64)
by Dorina Mitrea, Irina Mitrea, Marius Mitrea, and Michael Taylor
The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderon-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and rela...
Osserman Manifolds in Semi-Riemannian Geometry (Lecture Notes in Mathematics, #1777)
by Eduardo Garcia-Rio, Demir N. Kupeli, and Ramon Vazquez-Lorenzo
The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is...
In commemoration and celebration of the tenth anniversary of the Institute of Mathematics at East China Normal University, an International Conference on complex geometry and related fields recently convened. This collection presents some of the conference highlights, dealing with various and significant topics of differential and algebraic geometry, while exploring their connections to number theory and mathematical physics. Information for our distributors: Titles in this series are co-publish...
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formu...
Lectures On The Theory Of Group Properties Of Differential Equations
by Lev Vasilyevich Ovsyannikov
These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving sy...
This volume resulted from presentations given at the international "Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", that took place at the Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowne...