Invariant Theory of Variational Problems on Subspaces of a Riemannian Manifold
Author: Hanno Rund
Publisher:
Published: 1971
Total Pages: 60
ISBN-13:
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Tensors, Differential Forms, and Variational Principles
Author: David Lovelock
Publisher: Courier Corporation
Published: 2012-04-20
Total Pages: 402
ISBN-13: 048613198X
DOWNLOAD EBOOKIncisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Harmonic Maps: Selected Papers By James Eells And Collaborators
Author: James Eells
Publisher: World Scientific
Published: 1992-08-21
Total Pages: 453
ISBN-13: 9814506125
DOWNLOAD EBOOKThese original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.
Sixth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Gravitation And Relativistic Field Theories (In 2 Volumes)
Author: Humitaka Sato
Publisher: World Scientific
Published: 1993-01-08
Total Pages: 1797
ISBN-13: 9814554944
DOWNLOAD EBOOKThe Marcel Grossmann Meetings have been conceived with the aim of reviewing recent advances in gravitation and general relativity, with particular emphasis on mathematical foundations and physical predictions. The overall programme includes the broad categories of mathematical techniques, cosmology, quantum gravity, astrophysics, gravitational radiation and experimental developments.The proceedings contain invited and contributed papers.
Variational Problems in Riemannian Geometry
Author: Paul Baird
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 158
ISBN-13: 3034879687
DOWNLOAD EBOOKThis book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.
Variational Problems in Topology
Author: A.T. Fomenko
Publisher: Routledge
Published: 2019-06-21
Total Pages: 290
ISBN-13: 1351405675
DOWNLOAD EBOOKMany of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.
Harmonic Maps
Author: James Eells
Publisher: World Scientific
Published: 1992
Total Pages: 472
ISBN-13: 9789810207045
DOWNLOAD EBOOKThese original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.
American Doctoral Dissertations
Author:
Publisher:
Published: 1990
Total Pages: 768
ISBN-13:
DOWNLOAD EBOOKLectures on Geometric Variational Problems
Author: Seiki Nishikawa
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 160
ISBN-13: 4431684026
DOWNLOAD EBOOKIn this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments.
Geometric Control Theory and Sub-Riemannian Geometry
Author: Gianna Stefani
Publisher: Springer
Published: 2014-06-05
Total Pages: 385
ISBN-13: 331902132X
DOWNLOAD EBOOKHonoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.
