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Spherical Bernstein's Problem
The spherical Bernstein's problem is a possible generalization of the original Bernstein's problem in the field of global differential geometry, first proposed by Shiing-Shen Chern in 1969, and then later in 1970, during his plenary address at the International Congress of Mathematicians in Nice. The problem Are the equators in \mathbb^ the only smooth embedded minimal hypersurfaces which are topological n-dimensional spheres? Additionally, the spherical Bernstein's problem, while itself a generalization of the original Bernstein's problem, can, too, be generalized further by replacing the ambient space \mathbb^ by a simply-connected, compact symmetric space. Some results in this direction are due to Wu-Chung Hsiang and Wu-Yi Hsiang work. Alternative formulations Below are two alternative ways to express the problem: The second formulation Let the (''n'' − 1) sphere be embedded as a minimal hypersurface in S^n(1). Is it necessarily an equator? By the Almgren–Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein's Problem
In differential geometry, Bernstein's problem is as follows: if the graph of a function on R''n''−1 is a minimal surface in R''n'', does this imply that the function is linear? This is true for ''n'' at most 8, but false for ''n'' at least 9. The problem is named for Sergei Natanovich Bernstein who solved the case ''n'' = 3 in 1914. Statement Suppose that ''f'' is a function of ''n'' − 1 real variables. The graph of ''f'' is a surface in R''n'', and the condition that this is a minimal surface is that ''f'' satisfies the minimal surface equation :\sum_^ \frac\frac = 0 Bernstein's problem asks whether an ''entire'' function (a function defined throughout R''n''−1 ) that solves this equation is necessarily a degree-1 polynomial. History proved Bernstein's theorem that a graph of a real function on R2 that is also a minimal surface in R3 must be a plane. gave a new proof of Bernstein's theorem by deducing it from the fact that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Per Tomter
Per or PER may refer to: Places * Peru (IOC country code) * Pér, a village in Hungary * Perthshire (Chapman code), historic county in Scotland Science and technology * Physics education research * Packed Encoding Rules, in computing, an ASN.1 wire format * Per (storm), a January 2007 storm in Sweden Mathematics * Rate (mathematics), ratio between quantities in different units * Price–earnings ratio, in finance, a measure of growth in earnings * Player efficiency rating, a measure of basketball player performance * Partial equivalence relation, class of relations that are symmetric and transitive Science * Perseus (constellation) (standard astronomical abbreviation) * Period (gene) or ''per'', that regulates the biological clock and its corresponding protein PER * Protein efficiency ratio, of food * PER or peregrinibacteria, a candidate bacterial phylum Media and entertainment * PeR (band), a Latvian pop band * ''Per'' (film), a 1975 Danish film Transport * Perth Airport ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Problems
A mathematical problem is a problem that can be Representation (mathematics), represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the Orbit#Planetary orbits, orbits of the planets in the Solar System, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem referring to the Foundations of mathematics, nature of mathematics itself, such as Russell's Paradox. Real-world problems Informal "real-world" mathematical problems are questions related to a concrete setting, such as "Adam has five apples and gives John three. How many has he left?". Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problem (mathematics education), word problems, they are used in mathematics education to teach students to connect real-world situations to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annales Scientifiques De L'École Normale Supérieure
''Annales Scientifiques de l'École Normale Supérieure'' is a French scientific journal of mathematics published by the Société Mathématique de France. It was established in 1864 by the French chemist Louis Pasteur and published articles in mathematics, physics, chemistry, biology, and geology. In 1900, it became a purely mathematical journal. It is published with help of the Centre national de la recherche scientifique. Its web site is hosted by the mathematics department of the École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i .... External links * Archive(1864–2013) Mathematics journals Publications established in 1864 Multidisciplinary scientific journals Société Mathématique de France academic journals {{math-journal-stub English-F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematisches Forschungsinstitut Oberwolfach
The Oberwolfach Research Institute for Mathematics () is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do interdisciplinary, collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the Federal Ministry of Education and Research (Germany), German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazism, Nazis in order to further the German war ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugenio Calabi
Eugenio Calabi (May 11, 1923 – September 25, 2023) was an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications. Early life and education Calabi was born in Milan, Italy on May 11, 1923, into a Jewish family. His sister was the journalist Tullia Zevi Calabi. In 1938, the family left Italy because of the racial laws, and in 1939 arrived in the United States. In the fall of 1939, aged only 16, Calabi enrolled at the Massachusetts Institute of Technology, studying chemical engineering. His studies were interrupted when he was drafted in the US military in 1943 and served during World War II. Upon his discharge in 1946, Calabi was able to finish his bachelor's degree under the G.I. Bill, and was a Putnam Fellow. He received a master's degree in mathematics from the University of Illinois Urbana-Champaign in 1947 and his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frederick J
Frederick may refer to: People * Frederick (given name), the name Given name Nobility = Anhalt-Harzgerode = * Frederick, Prince of Anhalt-Harzgerode (1613–1670) = Austria = * Frederick I, Duke of Austria (Babenberg), Duke of Austria from 1195 to 1198 * Frederick II, Duke of Austria (1219–1246), last Duke of Austria from the Babenberg dynasty * Frederick the Fair (Frederick I of Austria (Habsburg), 1286–1330), Duke of Austria and King of the Romans = Baden = * Frederick I, Grand Duke of Baden (1826–1907), Grand Duke of Baden * Frederick II, Grand Duke of Baden (1857–1928), Grand Duke of Baden = Bohemia = * Frederick, Duke of Bohemia (died 1189), Duke of Olomouc and Bohemia = Britain = * Frederick, Prince of Wales (1707–1751), eldest son of King George II of Great Britain = Brandenburg/Prussia = * Frederick I, Elector of Brandenburg (1371–1440), also known as Frederick VI, Burgrave of Nuremberg * Frederick II, Elector of Brandenburg (1413–1470), Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-sphere
In mathematics, an -sphere or hypersphere is an - dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer . The circle is considered 1-dimensional and the sphere 2-dimensional because a point within them has one and two degrees of freedom respectively. However, the typical embedding of the 1-dimensional circle is in 2-dimensional space, the 2-dimensional sphere is usually depicted embedded in 3-dimensional space, and a general -sphere is embedded in an -dimensional space. The term ''hyper''sphere is commonly used to distinguish spheres of dimension which are thus embedded in a space of dimension , which means that they cannot be easily visualized. The -sphere is the setting for -dimensional spherical geometry. Considered extrinsically, as a hypersurface embedded in -dimensional Euclidean space, an -sphere is the locus of points at equal distance (the ''radius'') from a given '' center'' point. Its interior, consisting of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
