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An Introduction to Heisenberg Groups in Analysis and Geometry
"... Heisenberg groups, in discrete and continuous ..."
The Heisenberg group and . . .
, 2007
"... A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the “nonlinear σmodel” or “latticeCFT”, is given. Underlying this approach to CFT is a unitary modular functor, the construction of which follows from a “Quantization commutes with reduction” ..."
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” type of theorem for unitary quantizations of the moduli spaces of holomorphic torusbundles and actions of loop groups. This theorem in turn is a consequence of general constructions in the category of affine symplectic manifolds and their associated
Super Heisenberg Group
, 711
"... In this paper, we consider noncommutative superspace in relation with super Heisenberg group. We construct a matrix representation of super Heisenberg group and apply this to the twodimensional deformed N = (2, 2) superspace that appeared in string theory. We also construct a toy model for noncent ..."
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In this paper, we consider noncommutative superspace in relation with super Heisenberg group. We construct a matrix representation of super Heisenberg group and apply this to the twodimensional deformed N = (2, 2) superspace that appeared in string theory. We also construct a toy model for non
The Bernstein problem in the Heisenberg group
, 2005
"... We establish the following theorem of Bernstein type for the first Heisenberg group H¹: Let S be a C² connected Hminimal surface which is a graph over some plane P, then S is either a noncharacteristic vertical plane, or its generalized seed curve satisfies a type of constant curvature condition ..."
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Cited by 42 (10 self)
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We establish the following theorem of Bernstein type for the first Heisenberg group H¹: Let S be a C² connected Hminimal surface which is a graph over some plane P, then S is either a noncharacteristic vertical plane, or its generalized seed curve satisfies a type of constant curvature
LATTICE REPRESENTATIONS OF HEISENBERG GROUPS
, 2006
"... For any positive integers g and h, we consider the Heisenberg group (λ, µ, κ)  λ, µ ∈ R (h,g) , κ ∈ R (h,h) , κ + µ t λ symmetric Recall that the multiplication law is ..."
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Cited by 5 (5 self)
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For any positive integers g and h, we consider the Heisenberg group (λ, µ, κ)  λ, µ ∈ R (h,g) , κ ∈ R (h,h) , κ + µ t λ symmetric Recall that the multiplication law is
Convex Functions On The Heisenberg Group
 Calc. Var. Partial Differential Equations
"... Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial di#erential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group. 1. ..."
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Cited by 23 (2 self)
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Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial di#erential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group. 1.
An Introduction to Heisenberg Groups
, 2002
"... Actually, a number of related objects are often called “Heisenberg groups”, and they appear in several ways. Let n be a positive integer, and let λ be a positive real number. For ..."
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Actually, a number of related objects are often called “Heisenberg groups”, and they appear in several ways. Let n be a positive integer, and let λ be a positive real number. For
The Sasakian geometry of the Heisenberg group
 MR MR2554644
"... Abstract. In this note I study the Sasakian geometry associated to the standard CR structure on the Heisenberg group, and prove that the Sasaki cone coincides with the set of extremal Sasakian structures. Moreover, the scalar curvature of these extremal metrics is constant if and only if the metric ..."
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Cited by 6 (5 self)
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Abstract. In this note I study the Sasakian geometry associated to the standard CR structure on the Heisenberg group, and prove that the Sasaki cone coincides with the set of extremal Sasakian structures. Moreover, the scalar curvature of these extremal metrics is constant if and only if the metric
An Isoperimetric Inequality for the Heisenberg Groups
"... . We show that the Heisenberg groups H 2n+1 of dimension five and higher, considered as Riemannian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area ¸ L 2 ). This implies several important results about isoperimetric inequalit ..."
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Cited by 36 (0 self)
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. We show that the Heisenberg groups H 2n+1 of dimension five and higher, considered as Riemannian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area ¸ L 2 ). This implies several important results about isoperimetric
COMPENSATED COMPACTNESS AND THE HEISENBERG GROUP
"... Abstract. Jacobians of maps on the Heisenberg group are shown to map suitable group Sobolev spaces into the group Hardy space H 1. From this result and a weak ∗ convergence theorem for the Hardy space H 1 of the Heisenberg group, a compensated compactness property for these Jacobians is obtained. We ..."
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Cited by 3 (1 self)
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Abstract. Jacobians of maps on the Heisenberg group are shown to map suitable group Sobolev spaces into the group Hardy space H 1. From this result and a weak ∗ convergence theorem for the Hardy space H 1 of the Heisenberg group, a compensated compactness property for these Jacobians is obtained
Results 1  10
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1,247