Harmonic differential with prescribed singularities
نویسندگان
چکیده
منابع مشابه
Harmonic Maps with Prescribed Singularities on Unbounded Domains
The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ : R \Σ → H C into the (k+1)-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ : R \ Σ → H, where Σ is an unbounded smooth closed submanifold of R of codimension at...
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Let M a Riemannian manifold of dimension m ≥ 3, let Σ be a closed smooth submanifold of M of co-dimension at least 2, and let H be a Hadamard manifold with pinched sectional curvatures. We prove the existence and uniqueness of harmonic maps φ : M \ Σ → H with prescribed singularities along Σ. When M = R, and H = H C , the complex hyperbolic space, this result has applications to the problem of ...
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Let (M, g) be a classical Riemannian globally symmetric space of rank one and non-compact type. We prove the existence and uniqueness of solutions to the Dirichlet problem for harmonic maps into (M, g) with prescribed singularities along a closed submanifold of the domain. This generalizes our previous work where such maps into the hyperbolic plane were constructed. This problem, in the case wh...
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We find the minimal weighted energy ∫ Ω a(x)∣Du∣ of maps u ∶ Ω ⊂ Rm+n → S with prescribed singularities, where a(⋅) is a continuous positive weight. Our result extends previous ones of H. Brezis, J-M. Coron and E.H. Lieb (1986), G. Alberti, S. Baldo and G. Orlandi (2003), and V. Millot (2005).
متن کاملFunctions with prescribed singularities
The distributional k-dimensional Jacobian of a map u in the Sobolev space W 1,k−1 which takes values in the the sphere S can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M o...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1968
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1968-0222286-5