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10 papers · 1 filter
Intrinsic geometry of oriented congruences in three dimensions
C Denson Hill, Pawel Nurowski
Starting from the classical notion of an oriented congruence (i.e. a foliation by oriented curves) in , we abstract the notion of an oriented congruence structure. This is a 3…
A gap property for the growth of closed 3-manifold groups
Luca Fabrizio Di Cerbo
We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate o…
The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks
Claude LeBrun, L. J. Mason
We show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of t…
Convergence of compact Ricci solitons
Brian Weber
We show that sequences of compact gradient Ricci solitons converge to complete orbifold gradient solitons, assuming constraints on volume, the -norm of curvature, and the…
On Optimal 4-Dimensional Metrics
Claude LeBrun, Bernard Maskit
We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a…
The Complex Frobenius Theorem for Rough Involutive Structures
C. Denson Hill, Michael Taylor
We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the…