The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Shiing-shen Chern - One of the best experts on this subject based on the ideXlab platform.
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ON THE Riemann Mapping Theorem
The Annals of Mathematics, 1996Co-Authors: Shiing-shen ChernAbstract:We prove a generalization of the Riemann Mapping Theorem: if a bounded simply connected domain Q with connected smooth boundary has the spherical boundary, then it is biholomorphic to the unit ball.
Robert Rettinger - One of the best experts on this subject based on the ideXlab platform.
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Effective Riemann Mappings of multiply connected domains and Riemann surfaces
Mathematical Structures in Computer Science, 2016Co-Authors: Robert RettingerAbstract:We give new proofs of effective versions of the Riemann Mapping Theorem, its extension to multiply connected domains and the uniformization on Riemann surfaces. Astonishingly, in the presented proofs, we need barely more than computational compactness and the classical results.
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CiE - Compactness and the effectivity of uniformization
Lecture Notes in Computer Science, 2012Co-Authors: Robert RettingerAbstract:We give new proofs of effective versions of the Riemann Mapping Theorem, its extension to multiply connected domains and the uniformization on Riemann surfaces. Astonishingly, in the presented proofs we need barely more than computational compactness and the classical results.
José F. Escobar - One of the best experts on this subject based on the ideXlab platform.
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Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
The Annals of Mathematics, 1992Co-Authors: José F. EscobarAbstract:One of the most celebrated Theorems in mathematics is the Riemann Mapping Theorem. It says that an open, simply connected, proper subset of the plane is conformally diffeomorphic to the disk. In higher dimensions, very few regions are conformally diffeomorphic to the ball. However we can still ask whether a domain is conformally diffeomorphic to a manifold that resembles the ball in two ways, namely, it has zero scalar curvature and its boundary has constant mean curvature. In this paper we generalize the Riemann Mapping Theorem to higher dimensions in that sense.
Hemant Kumar Pathak - One of the best experts on this subject based on the ideXlab platform.
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Spaces of Analytic Functions
Complex Analysis and Applications, 2019Co-Authors: Hemant Kumar PathakAbstract:In this chapter, we shall put a metric on the set of all analytic functions on a fixed region \(G\subset \mathbb {C},\) and “compactness”, “converge”, “normality”, “uniform continuity”, and “equicontinuity” in this metric space is discussed. We shall also discuss Hurwitz’s Theorem, Montel’s Theorem and among the applications obtained is a proof of the Riemann Mapping Theorem.
Kang-tae Kim - One of the best experts on this subject based on the ideXlab platform.
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The Riemann Mapping Theorem from Riemann’s viewpoint
Complex Analysis and its Synergies, 2017Co-Authors: Robert E. Greene, Kang-tae KimAbstract:This article presents a rigorous proof of the Riemann Mapping Theorem via Riemann’s method, uncompromised by any appeals to topological intuition.
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the Riemann Mapping Theorem from Riemann s viewpoint
Complex Analysis and its Synergies, 2017Co-Authors: Robert E. Greene, Kang-tae KimAbstract:This article presents a rigorous proof of the Riemann Mapping Theorem via Riemann’s method, uncompromised by any appeals to topological intuition.
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The Riemann Mapping Theorem from Riemann's viewpoint
arXiv: Complex Variables, 2016Co-Authors: Robert E. Greene, Kang-tae KimAbstract:This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
