Liouville Theorems for Dirac - Harmonic Maps
نویسنده
چکیده
We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space Rn, the hyperbolic space Hn and a Riemannian manifold Sn (n ≥ 3) with the Schwarzschild metric to any Riemannian manifold N .
منابع مشابه
Regularity of Dirac-harmonic maps
For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...
متن کاملLiouville theorems for harmonic maps
Recently there has been much interest in the Liouville type theorems for harmonic maps. For a detailed survey and progress in this direction, see the works by Hildebrandt [4], Eells and Lemaire [2]. Here we would like to mention that for all known results, the conditions on the harmonic maps can be divided into two kinds. The first of these conditions concerns the finiteness of the energy of th...
متن کاملRegularity Theorems and Energy Identities for Dirac-harmonic Maps
We study Dirac-harmonic maps from a Riemann surface to a sphere Sn. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.
متن کاملNonlinear Dirac Equations on Riemann Surfaces
We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds. We provide the key analytical steps, i.e., small energy regularity and removable singularity theorems and energy identities for solutions.
متن کاملConvex Hull Properties of Harmonic Maps
In 1975, Yau [Y] proved, by way of a gradient estimate, that a complete manifold M with non-negative Ricci curvature must satisfy the strong Liouville property for harmonic functions. The strong Liouville property (Liouville property) asserts that any positive (bounded) harmonic function defined on M must be identically constant. In 1980, Cheng [C] generalized the gradient estimate to harmonic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008