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949
KSTABILITY OF CONSTANT SCALAR CURVATURE POLARIZATION
, 2008
"... In this paper, we shall show that a polarized algebraic manifold is Kstable if the polarization class admits a Kähler metric of constant scalar curvature. This generalizes the results of ChenTian [1], Donaldson [4] and Stoppa [20]. ..."
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Cited by 25 (1 self)
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In this paper, we shall show that a polarized algebraic manifold is Kstable if the polarization class admits a Kähler metric of constant scalar curvature. This generalizes the results of ChenTian [1], Donaldson [4] and Stoppa [20].
KSTABILITY AND PARABOLIC STABILITY
"... Abstract. Parabolic structures with rational weights encode certain iterated blowups of geometrically ruled surfaces. In this paper, we show that the three notions of parabolic polystability, Kpolystability and existence of constant scalar curvature Kähler metrics on the iterated blowup are equiv ..."
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Cited by 1 (0 self)
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Abstract. Parabolic structures with rational weights encode certain iterated blowups of geometrically ruled surfaces. In this paper, we show that the three notions of parabolic polystability, Kpolystability and existence of constant scalar curvature Kähler metrics on the iterated blowup
ON KSTABILITY OF REDUCTIVE VARIETIES
, 2003
"... Abstract. In [Don02], S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kähler metric of constant scalar curvature; and he partially confirmed it in the case of projective toric varieties. We extend Donaldson’s theory and computation ..."
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Abstract. In [Don02], S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kähler metric of constant scalar curvature; and he partially confirmed it in the case of projective toric varieties. We extend Donaldson’s theory
Kstability of constant scalar curvature Kähler manifolds
, 803
"... We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is Kstable. This refines the Ksemistability proved by S. K. Donaldson. 1 ..."
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We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is Kstable. This refines the Ksemistability proved by S. K. Donaldson. 1
On the Kstability of complete intersections in polarized manifolds
, 2008
"... We consider the problem of existence of constant scalar curvature Kähler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the a ..."
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Cited by 2 (0 self)
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We consider the problem of existence of constant scalar curvature Kähler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant
Extremal metrics and Kstability
, 2004
"... We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kähler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of KählerEinstein and constant scalar curvature metrics. We give a result in geometric invariant theory ..."
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Cited by 40 (2 self)
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We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kähler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of KählerEinstein and constant scalar curvature metrics. We give a result in geometric invariant theory
Kstability of constant scalar curvature Kähler manifolds, arXiv: math.AG/0803.4095
"... Abstract We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is Kstable. This refines the Ksemistability proved by S.K. Donaldson. ..."
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Cited by 52 (1 self)
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Abstract We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is Kstable. This refines the Ksemistability proved by S.K. Donaldson.
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 448 (2 self)
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constant scalar curvature one, and I has length 2ǫ −1; here ǫclose refers to C N topology, with N> ǫ −1. A parabolic neighborhood P(x, t, ǫ −1 r, r 2) is called a strong ǫneck, if, after scaling with factor r −2, it is ǫclose to the evolving standard neck, which at each
Conformal deformation of a Riemannian metric to constant curvature
 J. Diff. Geome
, 1984
"... A wellknown open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe&apos ..."
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Cited by 308 (0 self)
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A wellknown open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe
Results 1  10
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949