scholarly journals Removable Singularities of 𝒲𝒯-Differential Forms and Quasiregular Mappings

2007 ◽  
Vol 2007 ◽  
pp. 1-9
Author(s):  
Olli Martio ◽  
Vladimir Miklyukov ◽  
Matti Vuorinen
Keyword(s):  
Differential Forms ◽  
Quasiregular Mappings ◽  
Removable Singularities

scholarly journals Quasiregular mappings and 𝒲𝒯 -classes of differential forms on Riemannian manifolds

2002 ◽  
Vol 202 (1) ◽  
pp. 73-92 ◽  
Author(s):  
D. Franke ◽  
O. Martio ◽  
V.M. Miklyukov ◽  
M. Vuorinen ◽  
R. Wisk
Keyword(s):  
Riemannian Manifolds ◽  
Differential Forms ◽  
Quasiregular Mappings

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

scholarly journals Hardy Spaces for Quasiregular Mappings and Composition Operators

2021 ◽  
Author(s):  
Tomasz Adamowicz ◽  
María J. González
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Quasiconformal Mappings ◽  
Carleson Measures ◽  
Quasiregular Mappings ◽  
Classical Setting ◽  
Appl Math ◽  
Analytic Mappings

AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper $${\mathcal {H}}^p$$ H p -theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

Hamiltonian differential forms over the divided powers algebra

1986 ◽  
Vol 41 (2) ◽  
pp. 205-206
Author(s):  
M I Kuznetsov ◽  
S A Kirillov
Keyword(s):  
Differential Forms ◽  
Divided Powers
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