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An obstruction to the existence of constant scalar curvature Kähler metrics
, 2004
"... Abstract. We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subsc ..."
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Cited by 56 (6 self)
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Abstract. We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all
K"ahler metrics of constant scalar curvature on
"... Abstract It is shown that a Hirzebruch surface admits a K"ahler metric (possibly indefinite) of constant scalar curvature if and only if its degree equals zero. There have been many extensive studies for positivedefinite K"ahler metricsof constant scalar curvature, especially, K"ahle ..."
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Abstract It is shown that a Hirzebruch surface admits a K"ahler metric (possibly indefinite) of constant scalar curvature if and only if its degree equals zero. There have been many extensive studies for positivedefinite K"ahler metricsof constant scalar curvature, especially, K
PERTURBATIVE SOLUTIONS TO THE EXTENDED CONSTANT SCALAR CURVATURE EQUATIONS ON ASYMPTOTICALLY HYPERBOLIC MANIFOLDS
, 803
"... Abstract. We prove local existence of solutions to the extended constant scalar curvature equations introduced by A. Butscher, in the asymptotically hyperbolic setting. This gives a new local construction of asymptotically hyperbolic metrics with constant scalar curvature. ..."
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Abstract. We prove local existence of solutions to the extended constant scalar curvature equations introduced by A. Butscher, in the asymptotically hyperbolic setting. This gives a new local construction of asymptotically hyperbolic metrics with constant scalar curvature.
Blowing up and desingularizing constant scalar curvature Kähler manifolds
"... Abstract. This paper is concerned with the existence of constant scalar curvature Kähler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kähler metrics. We also consider the desingularization of isolated quotient singularities of compact ..."
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Cited by 33 (1 self)
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Abstract. This paper is concerned with the existence of constant scalar curvature Kähler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kähler metrics. We also consider the desingularization of isolated quotient singularities
Blowing up Kähler manifolds with constant scalar curvature II
, 2005
"... In this paper we prove the existence of Kähler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold which already carries a Kähler constant scalar curvature metric. Necessary conditions of the number and locations of the blow up points are given. ..."
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Cited by 14 (3 self)
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In this paper we prove the existence of Kähler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold which already carries a Kähler constant scalar curvature metric. Necessary conditions of the number and locations of the blow up points are given.
BLOWING UP AND DESINGULARIZING KÄHLER MANIFOLDS OF CONSTANT SCALAR CURVATURE
, 2005
"... In this paper we prove the existence of Kähler metrics of constant scalar curvature on blow ups at points and desingularizations of isolated quotient singularities of compact manifolds and orbifolds which already carry Kähler constant scalar curvature metrics. To describe our results let us recall t ..."
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In this paper we prove the existence of Kähler metrics of constant scalar curvature on blow ups at points and desingularizations of isolated quotient singularities of compact manifolds and orbifolds which already carry Kähler constant scalar curvature metrics. To describe our results let us recall
Constant scalar curvature metrics with isolated singularities
 Duke Math. Journal
, 1999
"... We extend the results and methods of [6] to prove the existence of constant positive scalar curvature metrics g which are complete and conformal to the standard metric on SN \ Λ, where Λ is a disjoint union of submanifolds of dimensions between 0 and (N − 2)/2. The existence of solutions with isolat ..."
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Cited by 37 (8 self)
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We extend the results and methods of [6] to prove the existence of constant positive scalar curvature metrics g which are complete and conformal to the standard metric on SN \ Λ, where Λ is a disjoint union of submanifolds of dimensions between 0 and (N − 2)/2. The existence of solutions
A REMARK ON KÄHLER METRICS OF CONSTANT SCALAR CURVATURE ON RULED COMPLEX SURFACES
, 2004
"... In this note we point out how some recent developments in the theory of constant scalar curvature Kähler metrics can be used to clarify the existence issue for such metrics in the special case of (geometrically) ruled complex surfaces. ..."
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Cited by 16 (4 self)
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In this note we point out how some recent developments in the theory of constant scalar curvature Kähler metrics can be used to clarify the existence issue for such metrics in the special case of (geometrically) ruled complex surfaces.
ENTIRE SCALAR CURVATURE FLOW AND HYPERSURFACES OF CONSTANT SCALAR CURVATURE IN MINKOWSKI SPACE
, 809
"... Abstract. We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that ..."
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Abstract. We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove
Solutions of the EinsteinDirac equation on Riemannian 3manifolds with constant scalar curvature
 J. Geom. Phys
"... This paper contains a classification of all 3dimensional manifolds with constant scalar curvature S ̸ = 0 that carry a nontrivial solution of the EinsteinDirac equation. ..."
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Cited by 4 (0 self)
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This paper contains a classification of all 3dimensional manifolds with constant scalar curvature S ̸ = 0 that carry a nontrivial solution of the EinsteinDirac equation.
Results 11  20
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8,548