Journal ArticleDOI
Boundary Value Problems for Dirac-Harmonic Maps and Their Heat Flows
Lei Liu,Miaomiao Zhu +1 more
TLDR
In this article, the authors discuss the latest progress on heat flow approaches for the existence of Dirac-harmonic maps under appropriate boundary conditions, and discuss the refined blow-up analysis for two types of approximating Diracharmonic mapping arising from those heat-flow approaches.Abstract:
Dirac-harmonic maps are critical points of an action functional that is motivated from the nonlinear σ-model of quantum field theory. They couple a harmonic map like field with a nonlinear spinor field. In this article, we shall discuss the latest progress on heat flow approaches for the existence of Dirac-harmonic maps under appropriate boundary conditions. Also, we discuss the refined blow-up analysis for two types of approximating Dirac-harmonic maps arising from those heat flow approaches.read more
References
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Journal ArticleDOI
The existence of minimal immersions of $2$-spheres
Jonathan Sacks,Karen Uhlenbeck +1 more
Book
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.
Book
Harmonic Maps of Manifolds with Boundary
TL;DR: In this article, the heat equation for manifolds and growth estimates and convergence of growth estimates are discussed.Harmonic maps, function spaces, Semi-elliptic and parabolic equations, and heat equation are presented.