26 citations · 47 across the 16 of their papers we have counts for
16 papers · 1 filter
Complete scalar-flat Kahler 4-manifolds with a continuous symmetry
Brian Weber
We study complete scalar-flat Kahler manifolds with a Killing field and a mild asymptotic condition. We show that topological and geometric rigidities exist that powerfully restric…
Asymptotic geometry of toric Kahler instantons
Brian Weber
The symplectic reduction of a complete toric Kähler manifold need not be closed or even be a polygon. Sharp differences in behavior occur between those complete toric Kähler 4-mani…
Pseudoconvex submanifolds in Kahler 4-manifolds
Brian Weber
On Kahler 4-manifolds, not necessarily compact or of finite topological type, we obtain relationships between the fundamental group of compact embedded Levi-flat or pseudoconvex su…
Canonical metrics and ambiKähler structures on 4-manifolds with symmetry
Keaton Naff, Brian Weber
For -invariant 4-metrics, we show that the -flat metrics are very different from the other canonical metrics (Bach-flat, Einstein, extremal Kähler, etc). We show every $…
A classification of scalar-flat toric Kähler instantons in dimension 4
Brian Weber
We classify all scalar-flat toric Kähler 4-manifolds under either of two asymptotic conditions: that the action fields decay slowly (or at all), or that the curvature decay is quad…
A Gap Theorem for Half-Conformally Flat Manifolds
Brian Weber, Martin Citoler-Saumell
We show that any compact half-conformally flat manifold of negative type, with bounded energy, sufficiently small scalar curvature, and a non-collapsing assumption, has all b…