We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension2 surgery technique which removes singular strata from fixed point free S-manifolds while preserving equivariant positive scalar curvature. These results are applied to derive the following generalization of a resu...

We prove the Gromov-Lawson-Rosenberg conjecture for cocompact Fuchsian groups, thereby giving necessary and sufficient conditions for a closed spin manifold of dimension greater than four with fundamental group cocompact Fuchsian to admit a metric of positive scalar curvature. Given a smooth closed manifold M, it is a long-standing question to determine whether or notM admits a Riemannian metri...

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 orbifolds which already carry constant scalar curvature Kähler metrics. Let (M,ω) be either a m-dimensiona...

In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show that the Whitehead manifold lacks such a metric, and in fact that R3 is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible noncompact manifolds of higher dimension exhibiting this curvature phenome...

We work primarily in the category of manifolds of bounded geometry. The objects are manifolds with bounds on the curvature tensor, its derivatives, and on the injectivity radius. The morphisms are diffeomorphisms of bounded distortion. We think of these manifolds as having a chosen bounded distortion class of metrics. Unless otherwise stated, all manifolds in the paper are assumed of this type....

Using a recent result of Bessières-Lafontaine-Rozoy, it is proved that any 3-manifold which admits a Yamabe metric of maximal positive scalar curvature is necessarily a spherical spaceform S/Γ, and the metric is the round metric on S/Γ. On all other 3-manifolds admitting a metric of positive scalar curvature, any maximizing sequence of Yamabe metrics has curvature diverging to infinity in L.

We study harmonic maps from a 3-manifold with boundary to $$\mathbb {S}^1$$ and prove special case of Gromov dihedral rigidity three-dimensional cubes whose angles are $$\pi / 2$$ . Furthermore, we give some applications mapping torus hyperbolic 3-manifolds.