# Kodaira dimension and the Yamabe problem

@article{Lebrun1997KodairaDA, title={Kodaira dimension and the Yamabe problem}, author={Claude Lebrun}, journal={Communications in Analysis and Geometry}, year={1997}, volume={7}, pages={133-156} }

The Yamabe invariant Y (M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M . (To be absolutely precise, one only considers constant-scalar-curvature metrics which are Yamabe minimizers, but this does not affect the sign of the answer.) If M is the underlying smooth 4-manifold of a complex algebraic surface (M,J), it is shown that the sign of Y (M) is completely determined by the Kodaira dimension… Expand

#### 96 Citations

Kodaira Dimension and the Yamabe Problem, II

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For compact complex surfaces (M4, J) of Kähler type, it was previously shown [31] that the sign of the Yamabe invariant Y (M) only depends on the Kodaira dimension Kod(M,J). In this paper, we prove… Expand

Kodaira Dimension & the Yamabe Problem , II

- 2021

For compact complex surfaces (M4, J) of Kähler type, it was previously shown [31] that the sign of the Yamabe invariant Y (M) only depends on the Kodaira dimension Kod(M,J). In this paper, we prove… Expand

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Abstract. The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of… Expand

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The Yamabe invariant is an invariant of a closed smooth manifold, which contains information about possible scalar curvature on it. It is well-known that a product manifold T^m\times B where T^m$ is… Expand

A ug 1 99 7 Yamabe Invariants and Spin c Structures

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The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds,… Expand

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Abstract We consider the equivariant Yamabe problem, i.e., the Yamabe problem on the space of G -invariant metrics for a compact Lie group G . The G -Yamabe invariant is analogously defined as the… Expand

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For a compact manifold M ofdim M=n≥4, we study two conformal invariants of a conformal class C on M. These are the Yamabe constant YC(M) and the Ln/2-norm WC(M) of the Weyl curvature. We prove that… Expand

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We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the… Expand

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