Search Results - "Donaldson, Simon"

Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry by Donaldson, Simon, Sun, Song

“…We prove a general result about the geometry of holomorphic line bundles over Kähler manifolds…”
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Atiyah's work on holomorphic vector bundles and gauge theories by Donaldson, Simon

“…The first part of the article surveys Atiyah’s work in algebraic geometry during the 1950s, mainly on holomorphic vector bundles over curves. In the second…”
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Introduction to the Atiyah issue by Donaldson, Simon

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Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2 and completion of the main proof by Chen, Xiuxiong, Donaldson, Simon, Sun, Song

“…This is the third and final article in a series which prove the fact that a K -stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider…”
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KÄHLER-EINSTEIN METRICS ON FANO MANIFOLDS. I: APPROXIMATION OF METRICS WITH CONE SINGULARITIES by CHEN, XIUXIONG, DONALDSON, SIMON, SUN, SONG

“…This is the first of a series of three papers which prove the fact that a K -stable Fano manifold admits a Kähler-Einstein metric. The main result of this…”
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KÄHLER-EINSTEIN METRICS ON FANO MANIFOLDS. II: LIMITS WITH CONE ANGLE LESS THAN 2π by CHEN, XIUXIONG, DONALDSON, SIMON, SUN, SONG

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Deformations Of Multivalued Harmonic Functions by Donaldson, Simon

“…Abstract We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as…”
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Closed 3‐forms in five dimensions and embedding problems by Donaldson, Simon, Lehmann, Fabian

“…We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the…”
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KÄHLER-EINSTEIN METRICS ON FANO MANIFOLDS. III: LIMITS AS CONE ANGLE APPROACHES 2π AND COMPLETION OF THE MAIN PROOF by CHEN, XIUXIONG, DONALDSON, SIMON, SUN, SONG

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Constant Scalar Curvature Metrics on Toric Surfaces by Donaldson, Simon K.

“… The main result of the paper is an existence theorem for a constant scalar curvature Kahler metric on a toric surface, assuming the K-stability of the…”
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Kähler–Einstein Metrics and Stability by Chen, Xiuxiong, Donaldson, Simon, Sun, Song

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Gromov-Hausdorff limits of Kaehler manifolds and algebraic geometry by Donaldson, Simon, Sun, Song

“…We prove a general result about the geometry of holomorphic line bundles over Kaehler manifolds…”
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Floer Homology Groups in Yang-Mills Theory by Donaldson, S. K.

“…The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed…”
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Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2 by Chen, Xiuxiong, Donaldson, Simon, Sun, Song

“…This is the second of a series of three papers which prove the fact that a K -stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider…”
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A journey through the mathematical world of Karen Uhlenbeck by Donaldson, Simon

“…This is an expository article discussing some of the work of Uhlenbeck, focusing mainly on work concerning harmonic maps and Yang-Mills fields…”
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The ADHM construction of Yang-Mills instantons by Donaldson, Simon

“…This is an expository article on the 1978 Atiyah-Drinfeld-Hitchin-Manin construction of Yang-Mills instanton connections over the 4-sphere…”
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Atiyah's work on holomorphic vector bundles and gauge theories by Donaldson, Simon

“…This article is a review of parts of Atiyah's work, mainly from the periods 1952-1958 and 1976-1990…”
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Fredholm topology and enumerative geometry: reflections on some words of Michael Atiyah by Donaldson, Simon

“…The first part of this article is a short and selective survey of developments in differential and algebraic geometry from the 1980's involving enumerative…”
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Calabi-Yau threefolds with boundary by Donaldson, Simon, Lehmann, Fabian

“…We develop the deformation theory of Calabi-Yau threefolds, by which we mean 3-dimensional complex manifolds with a nowhere-vanishing holomorphic 3-form, on…”
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Volume functionals on pseudoconvex hypersurfaces by Donaldson, Simon, Lehmann, Fabian

“…We study an intrinsic volume form defined on a pseudoconvex hypersurface in a complex Calabi-Yau manifold. We compute first and second variation formulae and…”
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