An Integral Formula for Singular Distributions
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DOI: 10.1007/s00025-019-1145-1
Abstract: The work is devoted to the differential geometry of singular distributions (i.e., of varying dimension) on a Riemannian manifold. We define such distributions as images of the tangent bundle with smooth endomorphisms. We introduce an… read more here.
Keywords: integral formula; formula singular; formula; singular distributions ... See more keywords
Cauchy Integral Formula for Fuchsian Groups. II
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DOI: 10.1007/s11785-025-01856-7
Abstract: We prove Conjecture 4.1 from (Kheifets, A.: Cauchy Integral Formula for Fuchsian Groups. Complex Anal. Oper. Theory 19(4), 71 (2025)) (Theorem 2.2 below): a generalization of the Hasumi’s Direct Cauchy Theorem property for the derivatives.… read more here.
Keywords: integral formula; fuchsian groups; formula fuchsian; theory ... See more keywords
The Cauchy Integral Formula, Quadrature Domains, and Riemann Mapping Theorems
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DOI: 10.1007/s40315-018-0246-2
Abstract: It is well known that a domain in the plane is a quadrature domain with respect to area measure if and only if the function z extends meromorphically to the double, and it is a… read more here.
Keywords: arc length; cauchy integral; integral formula; quadrature domains ... See more keywords
Boundary Integral Formula for Harmonic Functions on Riemann Surfaces
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DOI: 10.1007/s40315-020-00308-x
Abstract: We construct a boundary integral formula for harmonic functions on smoothly-bordered subdomains of Riemann surfaces embeddable into $${\mathbb {C}}{\mathbb {P}}^2$$ C P 2 . The formula may be considered as an analogue of the Green’s… read more here.
Keywords: harmonic functions; integral formula; formula; riemann surfaces ... See more keywords
An integral formula for a class of biharmonic maps from Euclidean 3-space
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DOI: 10.1016/j.difgeo.2018.07.001
Abstract: Abstract We classify biharmonic semi-conformal maps from domains of Euclidean 3-space whose fibres are arcs of circles in terms of holomorphic data. The geometry behind this classification enables us to give an integral formula which… read more here.
Keywords: biharmonic maps; geometry; integral formula; euclidean space ... See more keywords
The Cauchy integral formula and distributional integration
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DOI: 10.1080/17476933.2018.1557159
Abstract: ABSTRACT We study the Cauchy representation formula for analytic functions on the unit disc whose pointwise boundary value function is distributionally integrable. We prove that the formula holds when the distributional boundary values exist, and… read more here.
Keywords: cauchy integral; integral formula; formula; boundary values ... See more keywords