By Ilya J. Bakelman
Investigations in modem nonlinear research depend on principles, tools and prob lems from a variety of fields of arithmetic, mechanics, physics and different technologies. within the moment 1/2 the 20th century many popular, ex emplary difficulties in nonlinear research have been topic to extensive research and exam. The united rules and techniques of differential geometry, topology, differential equations and practical research in addition to different parts of study in arithmetic have been effectively utilized in the direction of the entire resolution of com plex difficulties in nonlinear research. it's not attainable to surround within the scope of 1 booklet all suggestions, rules, tools and effects concerning nonlinear research. for that reason, we will limit ourselves during this monograph to nonlinear elliptic boundary price difficulties in addition to worldwide geometric difficulties. so that we may well study those prob lems, we're supplied with a primary car: the speculation of convex our bodies and hypersurfaces. during this booklet we systematically current a chain of centrally major effects got within the moment half the 20 th century as much as the current time. specific consciousness is given to profound interconnections among a variety of divisions in nonlinear research. the idea of convex services and our bodies performs a vital position as the ellipticity of differential equations is heavily attached with the neighborhood and international convexity homes in their ideas. hence it's important to have a sufficiently great amount of fabric dedicated to the speculation of convex our bodies and services and their connections with partial differential equations.
By Robert Osserman
This hardcover version of A Survey of minimum Surfaces is split into twelve sections discussing parametric surfaces, non-parametric surfaces, surfaces that reduce quarter, isothermal parameters on surfaces, Bernstein's theorem, minimum surfaces with boundary, the Gauss map of parametric surfaces in E3, non-parametric minimum surfaces in E3, program of parametric surfaces to non-parametric difficulties, and parametric surfaces in En. For this version, Robert Osserman, Professor of arithmetic at Stanford collage, has considerably multiplied his unique paintings, together with the makes use of of minimum surfaces to settle vital conjectures in relativity and topology. He additionally discusses new paintings on Plateau's challenge and on isoperimetric inequalities. With a brand new appendix, supplementary references and accelerated index, this Dover version bargains a transparent, glossy and finished exam of minimum surfaces, offering critical scholars with primary insights into an more and more energetic and significant zone of arithmetic. Corrected and enlarged Dover republication of the paintings first released in e-book shape by way of the Van Nostrand Reinhold corporation, big apple, 1969. Preface to Dover variation. Appendixes. New appendix updating unique variation. References. Supplementary references. multiplied indexes.
By Olga Krupková (auth.)
The booklet offers a complete idea of ODE which come as Euler-Lagrange equations from as a rule higher-order Lagrangians. Emphasis is laid on employing equipment from differential geometry (fibered manifolds and their jet-prolongations) and international research (distributions and external differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi thought, etc., for any Lagrangian approach of any order are provided. the main concept - to accumulate those theories as similar with the category of similar Lagrangians - distinguishes this ebook from different texts on higher-order mechanics. The reader will be accustomed to parts of differential geometry, worldwide research and the calculus of variations.
By Phillip Griffiths, Daniel Grossman, Visit Amazon's Robert L. Bryant Page, search results, Learn about Author Central, Robert L. Bryant,
This well timed synthesis of partial differential equations and differential geometry should be of basic significance to either scholars and skilled researchers operating in geometric analysis.
By Yu. Aminov
Differential geometry is an actively constructing sector of contemporary arithmetic. This quantity offers a classical method of the final issues of the geometry of curves, together with the speculation of curves in n-dimensional Euclidean area. the writer investigates difficulties for exact periods of curves and offers the operating procedure used to acquire the stipulations for closed polygonal curves. The evidence of the Bakel-Werner theorem in stipulations of boundedness for curves with periodic curvature and torsion is usually provided. This quantity additionally highlights the contributions made via nice geometers. prior and current, to differential geometry and the topology of curves.
By S. Hyde, Z. Blum, T. Landh, S. Lidin, B.W. Ninham, S. Andersson, K. Larsson
This ebook develops the thesis that constitution and serve as in a number of condensed platforms - from the atomic assemblies in inorganic frameworks and natural molecules, via molecular self-assemblies to proteins - may be unified while curvature and floor geometry are taken including molecular form and forces. An staggering number of man made and organic assemblies should be adequately modelled and understood when it comes to hyperbolic surfaces, whose richness and wonder are just now being published via utilized mathematicians, physicists, chemists and crystallographers. those surfaces, frequently with reference to periodic minimum surfaces, weave and twist via house, carving out interconnected labyrinths whose diversity of topologies and symmetries problem the resourceful powers.
The ebook bargains an outline of those constructions and structural changes, convincingly demonstrating their ubiquity in covalent frameworks from zeolites used for cracking oil and toxins keep an eye on to enzymes and structural proteins, thermotropic and lyotropic bicontinuous mesophases shaped by means of surfactants, detergents and lipids, man made block copolymer and protein networks, in addition to organic cellphone assemblies, from muscular tissues to membranes in prokaryotic and eukaryotic cells. The relation among constitution and serve as is analysed when it comes to the formerly ignored
hidden variables of curvature and topology. hence, the catalytic task of zeolites and enzymes, the very best fabric homes of interpenetrating networks in microstructured polymer composites, the shipping necessities in cells, the transmission of nerve signs and the folding of DNA could be extra simply understood within the gentle of this.
The textual content is liberally sprinkled with figures and color plates, making it obtainable to either the start graduate scholar and researchers in condensed topic physics and chemistry, mineralogists, crystallographers and biologists.
By Arthur Jones, Alistair Gray, Robert Hutton
This ebook offers a simple creation to the speculation of differentiable manifolds. The authors then express how the speculation can be utilized to boost, easily yet carefully, the speculation of Lanrangian mechanics at once from Newton's legislation. pointless abstraction has been shunned to supply an account compatible for college kids in arithmetic or physics who've taken classes in complex calculus.
By F. Thomas Farrell
This ebook is an creation to the topological tension theorem for compact non-positively curved Riemannian manifolds. It incorporates a quickly casual account of the heritage fabric from surgical procedure concept and regulated topology prerequesite to this consequence. it really is meant for researchers and complex graduate scholars in either differential geometry and topology. This publication is the content material of a path given through the writer at TIFR in 1993.