By Mikhail Gromov, Jacques LaFontaine, Pierre Pansu, S. M. Bates, M. Katz, P. Pansu, S. Semmes
According to "Structures Mtriques des Varites Riemanninnes", edited through J. LaFontaine & P. Pansu.
Metric conception has gone through a dramatic part transition within the final many years whilst its concentration moved from the rules of genuine research to Riemannian geometry and algebraic topology, to the idea of countless teams and likelihood conception. the hot wave all started with seminal papers by way of Svarc and Milnor on progress of teams and the magnificent facts of the pressure of lattices via Mostow. This was once through the production of the asymptotic metric conception of countless teams by way of Gromov.
The structural metric method of the Riemannian classification, tracing again to Cheegers thesis, pivots round the suggestion of the Gromov-Hausdorff distance among Riemannian manifolds. This distance organizes Riemannian manifolds of all attainable topological forms right into a unmarried hooked up moduli house, the place convergence permits the cave in of size with unexpectedly wealthy geometry, as printed within the paintings of Cheeger, Fukaya, Gromov and Perelman. additionally, Gromov came across metric constitution inside of homotopy thought and therefore brought new invariants controlling combinatorial complexity of maps and areas, reminiscent of the simplicial quantity, that is answerable for levels of maps among manifolds. through the related interval, Banach areas and likelihood conception underwent a geometrical metamorphosis, encouraged through the Levy-Milman focus phenomenon, encompassing the legislation of huge numbers for metric areas with measures and dimensions going to infinity.
The first levels of the hot advancements have been offered in a direction introduced by way of Gromov in Paris, and become the recognized 1979 eco-friendly e-book by means of LaFontaine and Pansu. the current English translation of that paintings has been enriched and improved with new fabric to mirror fresh growth. also, 4 appendices---by Gromov on Levys inequality, by way of Pansu on quasiconvex domain names, by way of Katz on systoles of Riemannian manifolds, and through Semmes overviewing research on metric areas with measures---as good as an in depth bibliography and index around out this special and gorgeous booklet.
By A T Fomenko and Avgustin Tuzhilin, Visit Amazon's A.T. Fomenko Page, search results, Learn about Author Central, A.T. Fomenko, , Avgustin Tuzhilin
This ebook grew out of lectures offered to scholars of arithmetic, physics, and mechanics by way of A. T. Fomenko at Moscow college, below the auspices of the Moscow Mathematical Society. The ebook describes smooth and visible points of the speculation of minimum, two-dimensional surfaces in three-d house. the most subject matters coated are: topological homes of minimum surfaces, good and volatile minimum motion pictures, classical examples, the Morse-Smale index of minimum two-surfaces in Euclidean house, and minimum motion pictures in Lobachevskian house. Requiring just a commonplace first-year calculus and simple notions of geometry, this e-book brings the reader quickly into this attention-grabbing department of contemporary geometry.
By Y.G. Oh, K. Fukaya, Y-G Oh, K. Ono, G. Tian
Court cases of the 4th KIAS Annual overseas convention, held in August 14-18, 2000, Seoul, South Korea. best specialists within the box discover the more moderen advancements when it comes to homological replicate symmetry, Floer conception, D-branes and Gromov-Witten invariants.
By Izu Vaisman
The current paintings grew out of a research of the Maslov classification (e. g. (37]), that's a basic invariant in asymptotic research of partial differential equations of quantum physics. one of many many in terpretations of this category used to be given by way of F. Kamber and Ph. Tondeur (43], and it shows that the Maslov category is a secondary attribute category of a posh trivial vector package endowed with a true relief of its constitution staff. (In the fundamental paper of V. I. Arnold in regards to the Maslov type (2], it's also mentioned with out information that the Maslov category is attribute within the type of vector bundles pointed out pre viously. ) hence, we needed to check the complete diversity of secondary attribute periods concerned with this interpretation, and we gave a brief description of the implications in (83]. It grew to become out entire exposition of this thought was once relatively long, and, in addition, I felt that many strength readers must use loads of scattered references so as to locate the mandatory info from both symplectic geometry or the speculation of the secondary attribute sessions. at the otherhand, either those topics are of a miles greater curiosity in differential geome attempt to topology, and within the purposes to actual theories.
By Dirk J. Struik, Mathematics
First-class short advent provides basic thought of curves and surfaces and applies them to a couple of examples. themes contain curves, concept of surfaces, basic equations, geometry on a floor, envelopes, conformal mapping, minimum surfaces, extra. Well-illustrated, with ample difficulties and ideas. Bibliography.
By Luigi Bianchi
Questo secondo quantity riproduce in parte teorie speciali già svolte nella prima edizione del libro, che in questa costituivano i Capitoli da XI a XX, ed altre nuove ne accoglie.
By Claude Chevalley, Pierre Cartier, Catherine Chevalley
This quantity is the 1st in a projected sequence dedicated to the mathematical and philosophical works of the past due Claude Chevalley. It covers the most contributions by means of the writer to the idea of spinors. when you consider that its visual appeal in 1954, "The Algebraic conception of Spinors" has been a miles wanted reference. It provides the total tale of 1 topic in a concise and particularly transparent demeanour. The reprint of the booklet is supplemented by way of a sequence of lectures on Clifford Algebras given via the writer in Japan at in regards to the comparable time. additionally integrated is a postface via J.-P. Bourguignon describing the various makes use of of spinors in differential geometry constructed by way of mathematical physicists from the Nineteen Seventies to the current day. An insightful assessment of "Spinors" by means of J. Dieudonne can be made to be had to the reader during this new version.
By Nicole Berline
During this e-book, the Atiyah-Singer index theorem for Dirac operators on compact Riemannian manifolds and its newer generalizations obtain easy proofs. the most procedure that is used is an particular geometric development of the warmth kernels of a generalized Dirac operator. the 1st 4 chapters may be used on the textual content for a graduate path at the functions of linear elliptic operators in differential geometry and the single necessities are a familiarity with easy differential geometry. numerous chapters care for different preparatory fabric.