G. Robert Meyerhoff
department of mathematics
Professor and Assistant Chair, Graduate Programs
Ph.D. Princeton University
I study invariants of hyperbolic 3-manifolds; recently I’ve focused on the volume of hyperbolic 3-manifolds. The work of W. Thurston and G. Perelman shows that most 3-dimensional manifolds admit hyperbolic geometric structures. We can fruitfully study hyperbolic 3-manifolds by using the geometric structure to define invariants. The most natural such invariant is the volume, which simply uses the geometric structure to measure the size of the manifold. Thurston has shown that the volume invariant applied to the class of hyperbolic 3-manifolds produces a particularly rich collection of information.
- Minimum volume cusped hyperbolic three-manifolds, with D. Gabai and P. Milley,
J. Amer. Math. Soc. 22 (2009), 1157-1215.
- Homotopy hyperbolic 3-manifolds are hyperbolic, with D. Gabai and N. Thurston,
Annals of Math. 157 (2003), 335-431.
- The orientable cusped hyperbolic 3-manifolds of minimum volume, with C. Cao,
Invent. Math. 146 (2001), 451-478.
- Geometric invariants for 3-manifolds, The Mathematical Intelligencer, 14 (1992), 37-52.