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58 relations: Aldo Andreotti, André Lichnerowicz, Antiholomorphic function, Bernstein's problem, Cauchy–Riemann equations, Charles Epstein, Cohomology, Complex differential form, Complex manifold, Complexification, Convex set, Cotangent bundle, David Jerison, Differentiable manifold, Differential form, Differential operator, Dirichlet problem, Dolbeault cohomology, Edge-of-the-wedge theorem, Eugenio Elia Levi, Exterior algebra, Exterior derivative, François Trèves, Frobenius theorem (differential topology), H. Blaine Lawson, Hans Grauert, Hans Lewy, Heisenberg group, Hermitian manifold, Holomorphic function, Hypersurface, Implicit function theorem, Joseph J. Kohn, Kengo Hirachi, Laplace–Beltrami operator, Lars Hörmander, Line bundle, Louis Boutet de Monvel, Louis Nirenberg, Masatake Kuranishi, Mathematics, Mei-Chi Shaw, Minimal surface, Neumann boundary condition, Paul C. Yang, Plurisubharmonic function, Pseudoconvexity, Rauch comparison theorem, Real number, Riemannian geometry, ..., Sesquilinear form, Several complex variables, Stein manifold, Subbundle, Tangent bundle, Vector field, Yamabe problem, Yum-Tong Siu. Expand index (8 more) »
Aldo Andreotti
Aldo Andreotti (15 March 1924 – 21 February 1980) was an Italian mathematician who worked on algebraic geometry, on the theory of functions of several complex variables and on partial differential operators.
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André Lichnerowicz
André Lichnerowicz (January 21, 1915 – December 11, 1998) was a noted French differential geometer and mathematical physicist of Polish descent.
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Antiholomorphic function
In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions.
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Bernstein's problem
In differential geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function is linear? This is true in dimensions n at most 8, but false in dimensions n at least 9.
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Cauchy–Riemann equations
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.
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Charles Epstein
Charles L. Epstein is a Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, Philadelphia.
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Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.
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Complex differential form
In mathematics, a complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients.
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Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
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Complexification
In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Cotangent bundle
In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold.
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David Jerison
David Saul Jerison is an American mathematician, a professor of mathematics and a MacVicar Faculty Fellow at the Massachusetts Institute of Technology, and an expert in partial differential equations and Fourier analysis.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator.
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Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region.
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Dolbeault cohomology
In mathematics, in particular in algebraic geometry and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds.
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Edge-of-the-wedge theorem
In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge.
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Eugenio Elia Levi
Eugenio Elia Levi (18 October 1883 – 28 October 1917) was an Italian mathematician, known for his fundamental contributions in group theory, in the theory of partial differential operators and in the theory of functions of several complex variables: he was a younger brother of Beppo Levi and was killed in action during First World War.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Exterior derivative
On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.
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François Trèves
J.
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Frobenius theorem (differential topology)
In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations.
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H. Blaine Lawson
Herbert Blaine Lawson, Jr. is a mathematician best known for his work in minimal surfaces, calibrated geometry, and algebraic cycles.
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Hans Grauert
Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician.
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Hans Lewy
Hans Lewy (20 October 1904 – 23 August 1988) was a Jewish German born American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables.
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Heisenberg group
In mathematics, the Heisenberg group H, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form \end under the operation of matrix multiplication.
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Hermitian manifold
In mathematics, and more specifically in differential geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Hypersurface
In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.
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Implicit function theorem
In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables.
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Joseph J. Kohn
Joseph John Kohn (born May 18, 1932) is a Professor Emeritus of mathematics at Princeton University, where he researches partial differential operators and complex analysis.
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Kengo Hirachi
Kengo Hirachi (平地 健吾 Hirachi Kengo, born 30 November 1964) is a Japanese mathematician, specializing in CR geometry and mathematical analysis.
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Laplace–Beltrami operator
In differential geometry, the Laplace operator, named after Pierre-Simon Laplace, can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds.
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Lars Hörmander
Lars Valter Hörmander (24 January 1931 – 25 November 2012) was a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations".
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Line bundle
In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space.
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Louis Boutet de Monvel
Louis Boutet de Monvel (22 June 1941 – 25 December 2014) was a French mathematician who worked on functional analysis.
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Louis Nirenberg
Louis Nirenberg (born 28 February 1925) is a Canadian American mathematician, considered one of the outstanding analysts of the 20th century.
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Masatake Kuranishi
Masatake Kuranishi (倉西 正武 Kuranishi Masatake, born 19 July 1924, Tokyo) is a Japanese mathematician who works on several complex variables, partial differential equations, and differential geometry.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Mei-Chi Shaw
Mei-Chi Shaw is a professor of mathematics at the University of Notre Dame.
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Minimal surface
In mathematics, a minimal surface is a surface that locally minimizes its area.
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Neumann boundary condition
In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann.
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Paul C. Yang
Paul C. Yang is a Chinese-American mathematician specializing in differential geometry and partial differential equations.
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Plurisubharmonic function
In mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis.
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Pseudoconvexity
In mathematics, more precisely in the theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn.
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Rauch comparison theorem
In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch who proved it in 1951, is a fundamental result which relates the sectional curvature of a Riemannian manifold to the rate at which geodesics spread apart.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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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.
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Sesquilinear form
In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space.
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Several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions on the n-tuples of complex numbers.
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Stein manifold
In the theory of several complex variables and complex manifolds in mathematics, a Stein manifold is a complex submanifold of the vector space of n complex dimensions.
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Subbundle
In mathematics, a subbundle U of a vector bundle V on a topological space X is a collection of linear subspaces Ux of the fibers Vx of V at x in X, that make up a vector bundle in their own right.
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Tangent bundle
In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M. As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points x1 and x2 of manifold M the tangent spaces T1 and T2 have no common vector.
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Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
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Yamabe problem
The Yamabe problem in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature, and takes its name from the mathematician Hidehiko Yamabe.
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Yum-Tong Siu
Yum-Tong Siu (蕭蔭堂; born May 6, 1943 in Guangzhou, China) is the William Elwood Byerly Professor of Mathematics at Harvard University.
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CR geometry, CR structure, CR submanifold, CR-manifold, CR-structure, Cr submanifold, Cr-structure, Real-complex manifold.
References
[1] https://en.wikipedia.org/wiki/CR_manifold
