Steven Kerckhoff

Steven Paul Kerckhoff ( born 1952 in Madison ( Wisconsin)) is an American mathematician who deals with hyperbolic manifolds and Teichmüller theory.

Kerckhoff 1978 with William Thurston at Princeton University PhD (The asymptotic geometry of Teichmüller space). 1978/79 he was at the Institute for Advanced Study and later at the University of California, Berkeley. He is a professor at Stanford University.

In 1983 he proved a conjecture of Jakob Nielsen ( Nielsen realization problem). It asks whether a finite subgroup of the mapping class group of a surface can be realized as an isometry of a hyperbolic metric on the surface. Kerkhoff proved that this is possible. A previous proof attempt by Saul Kravetz 1959 turned in the 1970s as faulty out.

He wrote with William Floyd down a large part of the influential lectures (1978 /79) of Thurston Geometry and Topology of 3- Manifolds, Princeton.

It dealt with the development and the provision of strict evidence in the Thurston program, for example, with respect to the hyperbolic Dehn surgery of Thurston.

He was invited speaker at the International Congress of Mathematicians in 1983 in Warsaw.

He is also active in mathematics education for schools in California.

Writings

  • The geometry of Teichmüller space. Proceedings of the International Congress of Mathematicians, Vol 1, 2 ( Warsaw, 1983), 665-678, PWN, Warsaw, 1984.
  • Daryl Cooper, Craig D. Hodgson Three-dimensional orbifolds and cone - manifolds ( with afterword by Sadayoshi Kojima ), Mathematical Society of Japan Memoirs 5 Mathematical Society of Japan, Tokyo, 2000
  • The Nielsen realization problem-. Bull Amer. Math Soc. ( N.S. ) 2 ( 1980) no 3, 452-454.
  • The Nielsen realization problem-. Ann. of Math ( 2) 117 (1983 ), no 2, 235-265.
  • With Howard Masur, John Smillie Ergodicity of billiard flows and quadratic differentials, Ann. of Math ( 2) 124 (1986 ), 293-311.
  • With Thurston Noncontinuity of the action of the modular group at Bers ' boundary of Teichmüller space, Invent. Math 100 (1990), 25-47
  • Rigidity of hyperbolic cone with Hodgson - manifolds and hyperbolic Dehn surgery, J. Differential Geom 48 (1998), 1-59.
  • With Hodgson: Universal bounds for hyperbolic Dehn surgery. Ann. of Math ( 2) 162 (2005 ), no 1, 367-421.
Madison (Wisconsin) Jakob Nielsen (mathematician) William Floyd (mathematician)
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