Anthony Joseph Tromba

Anthony Joseph Tromba (born 10 August 1943, Brooklyn, New York City)[1] is an American mathematician, specializing in partial differential equations, differential geometry, and the calculus of variations.

Tromba received from Cornell University his bachelor's degree in 1965 and from Princeton University his M.S. in 1967 and his Ph.D. in 1968 under Stephen Smale with thesis Degree theory on Banach manifolds.[2] Tromba was from 1968 to 1970 an assistant professor at Stanford University. He became in 1970 an associate professor and in 1977 a full professor at the University of California, Santa Cruz.

He was in 1975 a visiting scholar at the Institute for Advanced Study, in 1970 a visiting professor at the University of Pisa, and in 1974 a visiting professor at the University of Bonn and at SUNY. In 1986 he was an Invited Speaker of the ICM in Berkeley, California.

Tromba's research deals with the applications of global nonlinear analysis to partial differential equations, with Morse theory for problems in the calculus of variations, and with questions concerning the properties of minimal surfaces in flat space and in Riemannian manifolds.[3]

He is also interested in a modern formulation of Teichmüller space from the point of view of Riemannian geometry, and its applications to minimal surfaces and physics. This approach constructs Teichmüller space directly as a differentiable manifold, and in so doing, completely bypasses the notions of quasi-conformal maps, the Beltrami equation, and nonstandard elliptic theory. As a consequence of this approach, several geometric descriptions of Teichmüller space as a differentiable manifold can be given.[3]

Selected publications

  • Teichmüller theory in Riemannian Geometry, Birkhäuser 1992[4]
  • with L. Andersson and V. Moncrief: On the global evolution problem in 2+1 gravity, J. Geometry and Physics, vol. 23, 1997, pp. 191–205
  • On a natural affine connector on the space of almost complex structures and the curvature of Teichmüller space with respect to its Weil-Petersson metric, Manuscripta Mathematica, vol. 56, 1996, pp. 475–497.
  • On the number of simply connected minimal surfaces spanning a curve, Memoirs AMS, No. 194, 1977
  • A general approach to Morse theory, J. Differential Geometry, vol. 12, 1977, pp. 47–85
  • with Friedrich Tomi: Existence theorems for minimal surfaces of non-zero genus spanning a contour, Memoirs AMS, No. 382, 1988
  • with F. Tomi: The index theorem for minimal surfaces of higher genus, Memoirs AMS, No. 560, 1995
  • with Stefan Hildebrandt: Mathematics and optimal form. Scientific American Books, New York NY 1985, ISBN 0-7167-5009-0 (French translation: Mathématiques et formes optimales. L'explication des structures naturelles. Pour la Science, Paris 1986, ISBN 2-902918-49-6; German translation: Panoptimum, Mathematische Grundmuster des Vollkommenen (= Spektrum-Bibliothek. vol. 12). Spektrum der Wissenschaft, Heidelberg 1987, ISBN 3-922508-82-0).
  • with Ulrich Dierkes and Stefan Hildebrandt: Global analysis of minimal surfaces, Springer Verlag 2010[5]
  • with Ulrich Dierkes and Stefan Hildebrandt: Regularity of Minimal Surfaces, Springer Verlag 2010[6]
  • with Kenneth McAloon: Calculus, Harcourt, Brace, Jovanovich 1972 (with the participation of Jerrold Marsden et al.)
  • with Kenneth McAloon Calculus of one variable, Harcourt, Brace, Jovanovich 1972 (with the participation of Jerrold Marsden et al.)
  • with Jerrold Marsden: Vector Calculus, Freeman, San Francisco, 5th edition 2003 (with the participation of Michael Hoffman and Joanne Seitz)
  • with Jerrold Marsden and Alan Weinstein: Basis multivariable calculus, Freeman 2000
  • Theory of Branched Minimal Surfaces, Springer Verlag 2012

References

  1. ↑ information from American Men and Women of Science, Thomson Gale 2004
  2. ↑ Anthony Joseph Tromba at the Mathematics Genealogy Project
  3. 1 2 "Anthony J. Tromba". U. C. Santa Cruz Mathematics Department.
  4. ↑ Wolf, Michael (1993). "Review of Teichmüller theory in Riemannian geometry by Anthony J. Tromba". Bull. Amer. Math. Soc. (N.S.). 29: 285–290. doi:10.1090/S0273-0979-1993-00421-X.
  5. ↑ Weber, Matthias (1 June 2010). "Review of Global Analysis of Minimal Surfaces by Ulrich Dierkes, Stefan Hildebrandt, and Anthony J. Tromba". MAA Reviews, Mathematical Association of America.
  6. ↑ Weber, Matthias (1 June 2010). "Review of Regularity of Minimal Surfaces by Ulrich Dierkes, Stefan Hildebrandt, and Anthony J. Tromba". MAA Reviews, Mathematical Association of America.
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