arXiv subjects

Benson Farb

Publications and source records attributed to Benson Farb.

75 records · Page 5Linked to original sources

arXiv2000

Harmonic Splittings of Surfaces

We give a proof, using harmonic maps from disks to real trees, of Skora's theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen): if G is the fundamental group of a surface of genus at least 2, then any small minimal G-action on a real tree is dual to the lift of a measured foliation. Analytic tools like the maximum principle are used to simplify the usual combinatorial topology arguments. Other analytic objects associated to a harmonic map, such as the Hopf differential and the moduli space of harmonic maps, are also introduced as tools for understanding the action of surface groups on trees.

math.DG↗

arXiv1998

Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, II

Let BS(1,n)= < a,b: aba^{-1}=b^n >. We prove that any finitely-generated group quasi-isometric to BS(1,n) is (up to finite groups) isomorphic to BS(1,n). We also show that any uniform group of quasisimilarities of the real line is bilipschitz conjugate to an affine group.

math.GR↗

arXiv1995

Filling-invariants at infinity for manifolds of nonpositive curvature

In this paper we construct and study isoperimetric functions at infinity for Hadamard manifolds. These quasi-isometry invariants give a measure of the spread of geodesics in such a manifold.

math.DG↗