Journal ArticleDOI
Energy identity and necklessness for $$\alpha $$ α -Dirac-harmonic maps into a sphere
TLDR
In this article, it was shown that the energy identity and necklessness hold during the interior blow-up process for a sequence of Dirac-harmonic maps from a Riemann surface M to a compact manifold N with uniformly bounded energy.Abstract:
Let $$(\phi _\alpha , \psi _\alpha )$$
be a sequence of $$\alpha $$
-Dirac-harmonic maps from a Riemann surface M to a compact Riemannian manifold N with uniformly bounded energy. If the target N is a sphere $$S^{K-1}$$
, we show that the energy identity and necklessness hold during the interior blow-up process as $$\alpha \searrow 1$$
for such a sequence .read more
Citations
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The qualitative behavior for 𝛼-harmonic maps from a surface with boundary into a sphere
TL;DR: In this article , a Riemannian manifold is represented as a sequence of Harmonic maps from a compact Rieman surface, and the authors propose an encoding scheme for the Harmonic Map of MathML.
On triviality of dirac-harmonic maps
TL;DR: In this article , it was shown that all Dirac-harmonic maps with compact domain are R -trivial and that this heat is just an extension of the classical heat flow for harmonic maps, for which short-time existence and uniqueness was proven by Chen, Jost, Sun and Zhu.
Are all Dirac-harmonic maps uncoupled?
TL;DR: In this article , it was shown that under some minimality assumption Dirac-harmonic maps defined on a closed domain are uncoupled, and they are defined as critical points of the super-symmetric energy functional.
References
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Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
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The existence of minimal immersions of $2$-spheres
Jonathan Sacks,Karen Uhlenbeck +1 more
Journal Article
Compensated compactness and Hardy spaces
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Quantum Fields and Strings: A Course for Mathematicians
TL;DR: The first truly comprehensive introduction to quantum field theory and perturbative string theory aimed at a mathematics audience can be found in this article, which offers a unique opportunity for mathematicians and mathematical physicists to learn about the beautiful and difficult subjects of quantum fields and string theory.
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Harmonic maps, conservation laws, and moving frames
TL;DR: In this article, the authors present Harmonic maps with symmetries, Harmonic map with symmetric and non-symmetric functions, compensations and exotic function spaces, and Surfaces with mean curvature.