A Liouville theorem on complete non-Kähler manifolds

Summary We study the problem of diffraction by a right-angled no-contrast penetrable wedge by means of a two-complex-variable Wiener–Hopf approach. Specifically, the analyticity properties of the unknown (spectral) functions of the two-complex-variable Wiener–Hopf equation are studied. We show that these spectral functions can be analytically continued onto a two-complex dimensional manifold, and unveil their singularities in C2. To do so, integral representation formulae for the spectral functions are given and thoroughly used. It is shown that the novel concept of additive crossing holds for the penetrable wedge diffraction problem, and that we can reformulate the physical diffraction problem as a functional problem using this concept.

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A Framework for Segmentation and Classification of Blood Cells Using Generative Adversarial Networks

Khan,

Shirazi,

Shahzad

et al. 2024

IEEE Access

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A Liouville theorem on complete non-Kähler manifolds

Abstract: In this paper, we prove a Liouville theorem for holomorphic functions on a class of complete Gauduchon manifolds. This generalizes a result of Yau for complete Kähler manifolds to the complete non-Kähler case.

Cited by 3 publications

References 19 publications

Stable Type Solutions of the Complex Laplacian Operators on Hermitian Manifolds

Stable Type Solutions of the Complex Laplacian Operators on Hermitian Manifolds

Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions

A Framework for Segmentation and Classification of Blood Cells Using Generative Adversarial Networks

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