51 citations · 373 across the 57 of their papers we have counts for
61 papers
An Overview of Einstein 4-Manifolds
Claude LeBrun
This expository article is based in part on the author's lecture series, "Einstein Metrics, Four-Manifolds, and Differential Topology," which was delivered as a 2026 Cours de la Ch…
Scalar Curvature and Product Manifolds
Claude LeBrun
We display 4-dimensional counter-examples to a restricted form of Rosenberg's S^1-Stability Conjecture recently proposed by Jie Xu. Namely, we show that there are smooth compact 4-…
Einstein Constants and Smooth Topology
Claude LeBrun
It was first shown in (Catanese-LeBrun 1997) that certain high-dimensional smooth closed manifolds admit pairs of Einstein metrics with Ricci curvatures of opposite sign. After rev…
Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces
Claude LeBrun
The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein-Hilbert functional. This article highlights the manner in wh…
Curvature in the Balance: The Weyl Functional and Scalar Curvature of 4-Manifolds
Claude LeBrun
The infimum of the Weyl functional is shown to be surprisingly small on many compact 4-manifolds that admit positive-scalar-curvature metrics. Results are also proved that systemat…
Twistors, Self-Duality, and Spin Structures
Claude LeBrun
The fact that every compact oriented 4-manifold admits spin structures was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither direct nor transparent. T…