The Weyl functional on 4-manifolds of positive Yamabe invariant

@article{Sung2021TheWF,
  title={The Weyl functional on 4-manifolds of positive Yamabe invariant},
  author={Chanyoung Sung},
  journal={Annals of Global Analysis and Geometry},
  year={2021}
}
  • Chanyoung Sung
  • Published 9 August 2021
  • Mathematics
  • Annals of Global Analysis and Geometry
W + g , χ ( M ) and τ ( M ) respectively, the self-dual Weyl tensor of g , the Euler characteristic and the signature of M . This generalizes M. J. Gursky inequality Math. (2) for the case of b 1 ( M ) > 0 in a much simpler way. He also extends all such lower bounds of the Weyl functional to 4-orbifolds including Gursky’s inequalities for the case of b +2 ( M ) > 0 or δ g W + g = 0 and obtain topological obstructions to the existence of self-dual orbifold metrics of positive scalar curvature. 

Fiberwise symmetrizations for variational problems on fibred manifolds and applications

We establish a framework for fiberwise spherical or planar symmetrization to find a lower bound of a Dirichlet-type energy functional in a variational problem on a fibred Riemannian manifold, and use

CR Yamabe constant and inequivalent CR structures

. CR Yamabe constant is an invariant of a compact CR manifold and can be used to distinguish CR structures. We construct a compact simply-connected 7-manifold admitting two strongly pseudoconvex CR

References

SHOWING 1-10 OF 47 REFERENCES

The Weyl functional near the Yamabe invariant

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

Monopole metrics and the orbifold Yamabe problem

We consider the self-dual conformal classes on n#CP^2 discovered by LeBrun. These depend upon a choice of n points in hyperbolic 3-space, called monopole points. We investigate the limiting behavior

Kodaira dimension and the Yamabe problem

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

Four-manifolds with positive Yamabe constant

We refine Theorem A due to Gursky \cite{G3}. As applications, we give some rigidity theorems on four-manifolds with postive Yamabe constant. In particular, these rigidity theorems are sharp for our

Computations of the orbifold Yamabe invariant

We consider the Yamabe invariant of a compact orbifold with finitely many singular points. We prove a fundamental inequality for the estimate of the invariant from above, which also includes a

Explicit Self-dual Metrics on Cp 2 # #cp 2

We display explicit half-conformally-flat metrics on the connected sum of any number of copies of the complex projective plane. These metrics are obtained from magnetic monopoles in hyperbolic

An index theorem on anti-self-dual orbifolds

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with singularities conjugate to ADE-type is proved. In 1988, Claude Lebrun gave examples of scalar-flat

Anti-self-dual orbifolds with cyclic quotient singularities

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to

Quotient singularities, eta invariants, and self-dual metrics

There are three main components to this article: (i) A formula for the eta invariant of the signature complex for any finite subgroup of ${\rm{SO}}(4)$ acting freely on $S^3$ is given. An