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Morrissey College of Arts and Sciences

G. Robert Meyerhoff

department of mathematics

Rob Meyerhoff picture 

Professor and Assistant Chair, Graduate Programs

Ph.D. Princeton University


Professional History

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.

Selected publications

  • 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.