2018
DOI: 10.1112/plms.12132
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Construction of constant scalar curvature Kähler cone metrics

Abstract: Abstract. Over a compact Kähler manifold, we provide a Fredholm alternative result for the Lichnerowicz operator associated to a Kähler metric with conic singularities along a divisor. We deduce several existence results of constant scalar curvature Kähler metrics with conic singularities: existence result under small deformations of Kähler classes, existence result over a Fano manifold, existence result over certain ruled manifolds. In this last case, we consider the projectivisation of a parabolic stable hol… Show more

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Cited by 7 publications
(16 citation statements)
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References 55 publications
(182 reference statements)
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“…Since we can expand τ and ϕ(τ ) in the powers of |z 1 | 2β , we see from the estimates for g ϕ that the Kähler potential for ω ϕ is an element of C 4,α,β as defined e.g. in [29,36].…”
Section: Some Properties Of Momentum-constructed Metrics With ϕ (B) =mentioning
confidence: 99%
“…Since we can expand τ and ϕ(τ ) in the powers of |z 1 | 2β , we see from the estimates for g ϕ that the Kähler potential for ω ϕ is an element of C 4,α,β as defined e.g. in [29,36].…”
Section: Some Properties Of Momentum-constructed Metrics With ϕ (B) =mentioning
confidence: 99%
“…The proof of this lemma is similar to the proof of the Proposition 3.1 in [44]. We could replace W 2,p,β s with C 1,α,β and use the compactness argument of C 1,α,β .…”
Section: 3mentioning
confidence: 88%
“…We define the spaces C 4,α,β (ω) in Section 2 in [47] and Section 2 in [44], the function in which has all their 4th order derivatives in C 0,α,β . The idea is firstly to define a local 4th order Hölder space with respect to the flat cone metric ω β near the cone points.…”
Section: Linear Theory Of Lichnerowicz Operatorsmentioning
confidence: 99%
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