Dennis Deturk is an American mathematician. Best known for the so-called "trick Deturka", which allowed to simplify the proof of the existence of the Ricci stream .
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Biography
He graduated in 1976 from the with a bachelor's degree. He defended his thesis in 1980 at the University of Pennsylvania under the leadership of Jerry Kazhdan .
As of the mid-2010s, he was a professor of mathematics at the University of Pennsylvania [2] .
Scientific Contribution
- Trick Deturka - allows you to simplify the proof of the existence of the Ricci stream . The Ricci flow is not a parabolic equation ; Deturk found a parabolic equation whose solutions are isometric to the solution of the Ricci flow. Thus, the question of the existence of a Ricci flow was reduced to the already well-known question of parabolic equations.
- Together with Jerry Kazhdan , he proved the result obtained earlier by Scheffel that harmonic coordinates give an atlas of the highest degree of smoothness for a given Riemannian manifold [3] [4] .
Recognition
- In 2002, he was awarded Mathematical Association of America for teaching [5] .
- In January 2012, he shared with three co-authors [6] [7] .
- In 2012, he became a full member of the American Mathematical Society [8] .
Selected Publications
- Dennis M. DeTurck, Existence of metrics with prescribed Ricci curvature: local theory. Invent. Math. 65 (1981/82), no. 1, 179-207.
- Dennis M. DeTurck, Deforming metrics in the direction of their Ricci tensors. J. Differential Geom. 18 (1983), no. 1, 157-162.
Notes
- ↑ Mathematical Genealogy - 1997.
- ↑ House Staff, Riepe College House, U. of Penn. . Archived on November 14, 2012.
- ↑ Shefel, S. Z. “Conformal correspondence of metrics and smoothness of isometric immersions.” Siberian Mathematical Journal 20.2 (1979): 397-401.
- ↑ Dennis DeTurck, Jerry Kazdan Some regularity theorems in Riemannian geometry. Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 3, 249-260.
- ↑ The Mathematical Association of America's Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics . MAA Online . The Mathematical Association of America (April 10, 2007). - "... in order to honor college or university teachers who have been widely recognized as extraordinarily successful and whose teaching effectiveness has been shown to have had influence beyond their own institutions.". Date of treatment December 26, 2007.
- ↑ January 30, 2012, Penn News, Penn Mathematcians Win 2012 Chauvenet Prize
- ↑ DeTurck, Dennis; Gluck, Herman; Pomerleano, Daniel; Vela-Vick, Shea. The Four Vertex Theorem and Its Converse (English) // Notices of the American Mathematical Society : journal. - 2007. - Vol. 54 , no. no. 2 . - P. 192-207 .
- ↑ List of Fellows of the American Mathematical Society , retrieved 2012-11-10.