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Metric Structures For Riemannian And Non-Riemannian Spaces
''Metric Structures for Riemannian and Non-Riemannian Spaces'' is a book in geometry by Mikhail Gromov. It was originally published in French in 1981 under the title ''Structures métriques pour les variétés riemanniennes'', by CEDIC (Paris). History The 1981 edition was edited by Jacques Lafontaine and Pierre Pansu. The English version, considerably expanded, was published in 1999 by Birkhäuser Verlag, with appendices by Pierre Pansu, Stephen Semmes, and Mikhail Katz. The book was well received by Mircea Craioveanu ('' Zentralblatt Math
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Mikhail Gromov (mathematician)
Mikhael Leonidovich Gromov (also Mikhail Gromov, Michael Gromov or Misha Gromov; russian: link=no, Михаи́л Леони́дович Гро́мов; born 23 December 1943) is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of IHÉS in France and a professor of mathematics at New York University. Gromov has won several prizes, including the Abel Prize in 2009 "for his revolutionary contributions to geometry". Biography Mikhail Gromov was born on 23 December 1943 in Boksitogorsk, Soviet Union. His Russian father Leonid Gromov and his Jewish mother Lea Rabinovitz were pathologists. His mother was the cousin of World Chess Champion Mikhail Botvinnik, as well as of the mathematician Isaak Moiseevich Rabinovich. Gromov was born during World War II, and his mother, who worked as a medical doctor in the Soviet Army, had to leave the front line in order to give birth to him. When Gromov was nine years old, his mother ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhäuser Verlag
Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (particularly: history of science, geosciences, computer science) and mathematics books and journals under the Birkhäuser imprint (with a leaf logo) sometimes called Birkhäuser Science. * Birkhäuser Verlag – an architecture and design publishing company was (re)created in 2010 when Springer sold its design and architecture segment to ACTAR. The resulting Spanish-Swiss company was then called ActarBirkhäuser. After a bankruptcy, in 2012 Birkhäuser Verlag was sold again, this time to De Gruyter. Additionally, the Reinach-based printer Birkhäuser+GBC operates independently of the above, being now owned by ''Basler Zeitung''. History The original Swiss publishers program focused on regional literature. In the 1920s the sons of Emil Birkh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Leonidovich Gromov
Mikhael Leonidovich Gromov (also Mikhail Gromov, Michael Gromov or Misha Gromov; russian: link=no, Михаи́л Леони́дович Гро́мов; born 23 December 1943) is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of IHÉS in France and a professor of mathematics at New York University. Gromov has won several prizes, including the Abel Prize in 2009 "for his revolutionary contributions to geometry". Biography Mikhail Gromov was born on 23 December 1943 in Boksitogorsk, Soviet Union. His Russian father Leonid Gromov and his Jewish mother Lea Rabinovitz were pathologists. His mother was the cousin of World Chess Champion Mikhail Botvinnik, as well as of the mathematician Isaak Moiseevich Rabinovich. Gromov was born during World War II, and his mother, who worked as a medical doctor in the Soviet Army, had to leave the front line in order to give birth to him. When Gromov was nine years old, his mother ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques Lafontaine
Ancient and noble French family names, Jacques, Jacq, or James are believed to originate from the Middle Ages in the historic northwest Brittany region in France, and have since spread around the world over the centuries. To date, there are over one hundred identified noble families related to the surname by the Nobility & Gentry of Great Britain & Ireland. Origins The origin of this surname ultimately originates from the Latin, Jacobus which belongs to an unknown progenitor. Jacobus comes from the Hebrew name, Yaakov, which translates as "one who follows" or "to follow after". Ancient history A French knight returning from the Crusades in the Holy Lands probably adopted the surname from "Saint Jacques" (or "James the Greater"). James the Greater was one of Jesus' Twelve Apostles, and is believed to be the first martyred apostle. Being endowed with this surname was an honor at the time and it is likely that the Church allowed it because of acts during the Crusades. Indeed, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Pansu
Pierre Pansu (born 13 July 1959) is a French mathematician and a member of the Arthur Besse group and a close collaborator of Mikhail Gromov. He is a professor at the Université Paris-Sud 11 and the École Normale Supérieure in Paris. His main research field is geometry. His contribution to mathematics was celebrated by a double event (a conference and a workshop) co-organized for his 60th birthday by the Clay Mathematics Institute. Pierre Pansu is the grandson of French physician Félix Esclangon, and the great grand-nephew of mathematician and astronomer Ernest Esclangon, inventor of the talking clock, and brother of Robert Pansu, chemist and research director at CNRS. See also * Metric Structures for Riemannian and Non-Riemannian Spaces *Pansu derivative References *. * Prix Georges Charpak 2013 Académie des Sciences, France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Semmes
Stephen William Semmes (born 26 May 1962) is the Noah Harding Professor of Mathematics at Rice University. He is known for contributions to analysis on metric spaces, as well as harmonic analysis, complex variables, partial differential equations, and differential geometry. He received his B.S. at the age of 18, a Ph.D. at 21 from Washington University in St. Louis and became a full professor at Rice at 25. Awards Semmes was awarded a Sloan Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ... in 1987. In 1994, he gave an invited talk at the International Congress of Mathematicians. Publications * Coifman, R.; Lions, P.-L.; Meyer, Y.; Semmes, S.: Compensated compactness and Hardy spaces. J. Math. Pures Appl. (9) 72 (1993), no. 3, 247–286. * David, Guy; Semmes, St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Katz
Mikhail "Mischa" Gershevich Katz (born 1958, in Chișinău)Curriculum vitae retrieved 2011-05-23. is an Israeli , a professor of mathematics at . His main interests are , and |
MathSciNet
MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links to other MR entries, citations, full journal entries, and links to original articles. It contains almost 3.6 million items and over 2.3 million links to original articles. Along with its parent publication ''Mathematical Reviews'', MathSciNet has become an essential tool for researchers in the mathematical sciences. Access to the database is by subscription only and is not generally available to individual researchers who are not affiliated with a larger subscribing institution. For the first 40 years of its existence, traditional typesetting was used to produce the Mathematical Reviews journal. Starting in 1980 bibliographic information and the reviews themselves were produced in both print and electronic form. This formed the basis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zentralblatt Math
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic. History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix Klein, the great ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemannian Geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "''Ueber die Hypothesen, welche der Geometrie zu Grunde liegen''" ("On the Hypotheses on which Geometry is Based.") It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
