Overview
The Department is saddened by the passing of our friend and colleague Cliff Earle. Read more.
Research Focus
Complex variables, Teichmüller spaces
Most of my research concerns invariants belonging to Riemann surfaces. I am especially interested in learning how these invariants change when the complex structure of the Riemann surface is modified. A useful technique is to consider a family of Riemann surfaces depending holomorphically on some parameters and to study how the invariants of the surface change as we move about in the parameter space. Quasiconformal maps and Kleinian groups have proved to be fundamental tools for the construction of good parameter spaces, so I have studied and used them extensively.
Publications
- A fibre bundle description of Teichmüller theory (with J. Eells, Jr.), J. Diff. Geom. 3 (1969), 19–43.
- Families of Riemann surfaces and Jacobi varieties, Ann. Math. 107 (1978), 255–286.
- Conformally natural extension of homeomorphisms of the circle (with A. Douady), Acta Math. 157 (1986), 23–48.
- Holomorphic motions and Teichmüller spaces (with I. Kra and S. L. Krushkal), Trans. Amer. Math. Soc. 343 (1994), 927–948.
- Geometric isomorphisms between infinite dimensional Teichmüller spaces(with F. P. Gardiner), Trans. Amer. Math. Soc. 348 (1996), 1163–1190.
