Cauchy-Riemann ̄∂-equations with some applications

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2022-01-01 DOI:10.1515/coma-2021-0134

J. Xiao, Cheng Yuan

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引用次数: 2

Abstract

Abstract This paper shows that given 0 < p < 3 and a complex Borel measure µ on the unit disk 𝔻 the inhomogeneous Cauchy-Riemann ̄∂-equation ∂z¯u(z)=dμ(z)(2πi)-1dz¯∧dz {\partial _{\bar z}}u\left( z \right) = {{d\mu \left( z \right)} \over {{{\left( {2\pi i} \right)}^{ - 1}}d\bar z \wedge dz}} − a complex Gauss curvature of the weighted disk (𝔻, µ) ᗄ z ∈ 𝔻, has a distributional solution (initially defined on ̄𝔻 = 𝔻 ∪ 𝕋) u ∈ ℒ2,p(𝕋) (formed of: (i) Morrey’s space M2,0

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.

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