Jürgen Moser
Jürgen K. Moser | |
|---|---|
Outer billiard Volterra lattice Calogero–Moser system Chern–Moser invariants De Giorgi–Nash–Moser estimates Moser normal form Moser iteration Moser's trick Moser twist theorem | |
| Awards | George David Birkhoff Prize (1968) James Craig Watson Medal (1969) Wolf Prize (1994/1995) MIT, ETH Zurich |
| Doctoral advisor | Franz Rellich Carl Ludwig Siegel |
| Doctoral students | Charles Conley Håkan Eliasson |
| Other notable students | Paul Rabinowitz |
Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-American
partial differential equations
.
Life
Moser's mother Ilse Strehlke was a
German Army and died in Schloßberg during the East Prussian offensive
.
Moser married the biologist Dr. Gertrude C. Courant (
.Work
Moser completed his undergraduate education at and received his
ETH Zürich mathematics faculty. Moser was president of the International Mathematical Union
in 1983–1986.
Research
In 1967,
Sobolev embedding theorem.[2] Moser found the sharp constant in Trudinger's inequality, with the corresponding result often known as the Moser–Trudinger inequality.[3]
Elliptic and parabolic partial differential equations
In the late 1950s,
Harnack inequality.[2][4] In his original work, a key role was played by an extension of the John–Nirenberg lemma. Enrico Bombieri
later found an argument avoiding this lemma in the elliptic case, which Moser was able to adapt to the parabolic case. The collection of these regularity results are often known as De Giorgi–Nash–Moser theory, although the original results were due solely to De Giorgi and Nash.
Differential geometry
In 1965, Moser found new results showing that any two
cohomologous family of symplectic forms are related to one another by diffeomorphisms: this is also known as Moser's stability theorem.[6] Moser also analyzed the case of manifolds with boundary, although his argument was mistaken. Later, with Bernard Dacorogna
, Moser fully carried out the analysis of the boundary case.
Moser also made an early contribution to the
Riemannian metrics on the projective plane, every function except for those which are nonpositive arises as a scalar curvature.[7]
Moser's prior analysis of the Moser–Trudinger inequality was important for this work, highlighting the geometric significance of optimal constants in functional inequalities.
Research of
CR geometry, dealing with three-dimensional hypersurfaces of smooth four-dimensional manifolds which are also equipped with a complex structure. They had identified local invariants distinguishing two such structures, analogous to prior work identifying the Riemann curvature tensor and its covariant derivatives as fundamental invariants of a Riemannian metric. With Shiing-Shen Chern, Moser extended Poincaré and Cartan's work to arbitrary dimensions. Their work has had a significant influence on CR geometry.[8][9]
Students
Among Moser's students were Mark Adler of
University of Wisconsin
.
Awards and honours
Moser won the first
University of Bochum and from Pierre and Marie Curie University in Paris. The Society for Industrial and Applied Mathematics
established a lecture prize in his honor in 2000.
Major publications
Articles
- Moser, Jürgen (1960). "A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations". Zbl 0111.09301.
- Moser, Jürgen (1961). "A new technique for the construction of solutions of nonlinear differential equations". Zbl 0104.30503.
- Moser, Jürgen (1961). "On Harnack's theorem for elliptic differential equations". Zbl 0111.09302.
- Moser, J. (1962). "On invariant curves of area-preserving mappings of an annulus". Nachrichten der Akademie der Wissenschaften zu Göttingen. II. Mathematisch–Physikalische Klasse: 1–20. Zbl 0107.29301.
- Moser, J. (2001). "Remark on the paper: On invariant curves of area-preserving mappings of an annulus". Regular and Chaotic Dynamics. 6 (3): 337–338. Zbl 0992.37053.
- Moser, J. (2001). "Remark on the paper: On invariant curves of area-preserving mappings of an annulus". Regular and Chaotic Dynamics. 6 (3): 337–338.
- Moser, Jürgen (1964). "A Harnack inequality for parabolic differential equations". )
- Moser, Jürgen (1965). "On the volume elements on a manifold". Zbl 0141.19407.
- Moser, Jürgen (1966). "A rapidly convergent iteration method and non-linear partial differential equations. I". Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie III. 20 (2): 265–315. Zbl 0144.18202.
- Moser, Jürgen (1966). "A rapidly convergent iteration method and non-linear differential equations. II". Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie III. 20 (3): 499–535. Zbl 0144.18202.
- Moser, J. (1971). "A sharp form of an inequality by N. Trudinger". Zbl 0213.13001.
- Moser, J. (1971). "On a pointwise estimate for parabolic differential equations". Zbl 0227.35016.
- Moser, J. (1973). "On a nonlinear problem in differential geometry". In Zbl 0275.53027.
- )
- Zbl 0707.35041.
Books
- Moser, Jürgen K. (1968). Lectures on Hamiltonian systems. Zbl 1415.00008.
- Zbl 0312.70017.
- Moser, Jürgen (1973). Stable and random motions in dynamical systems. With special emphasis on celestial mechanics. Annals of Mathematics Studies. Vol. 77. Princeton, NJ: Zbl 0271.70009.
- Moser, Jürgen; Zbl 1087.37001.
Notes
- ^ "Jurgen Kurt Moser". U.S. Naturalization Records Indexes, 1794–1995. Ancestry.com. Retrieved June 12, 2011.
Name: Jurgen Kurt Moser; Age: 31; Birth Date: 4 Jul 1928; Issue Date: 2 Feb 1959; State: Massachusetts; Locality, Court: District of Massachusetts, District Court
(subscription required) - ^ Zbl 1042.35002.
- Zbl 0978.53002.
- MR 1465184.
- Zbl 1156.53003.
- Zbl 1380.53003.
- Zbl 0896.53003.
- doi:10.2307/1970961)
- Zbl 0712.32001.
- ^ Moser, J. (1979). "The holomorphic equivalence of real hypersurfaces". Proceedings of the International Congress of Mathematicians (Helsinki, 1978). pp. 659–668.
- ^ Moser, Jürgen (1998). "Dynamical systems — past and present". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I. pp. 381–402.
References
- Mather, John N.; McKean, Henry P.; Nirenberg, Louis; Rabinowitz, Paul H. (December 2000). "Jürgen K. Moser" (PDF). Notices of the AMS. 4 (11): 1392–1405. Retrieved 2007-08-20.
- J.J. O'Connor; E. F. Robertson. "Jürgen Kurt Moser". Retrieved 2008-07-04.
- Sylvia Nasar (December 21, 1999). "Obituary, New York Times". The New York Times. Retrieved 2010-09-14.
- American Institute of Physics. "Professional biography Jürgen Moser". Archived from the original on 2012-10-05. Retrieved 2010-12-05.
- Vladimir Arnold (2000). "Déclin des Mathématiques (après la mort de Jürgen Moser)" (PDF). La Gazette des mathématiciens (in French). 84: 92–94. Archived from the original (PDF) on 2014-08-08.
- ETH (20 March 2002). "Biography of Jürgen Moser, by ETH". ETH. Retrieved 2013-04-02.
- Guardian (20 March 2000). "Obituary of Moser, by Guardian". The Guardian. Retrieved 2013-05-27.
- SIAM (20 April 2001). "Moser Lecture, by SIAM". Retrieved 2013-11-16.
- Max Planck Institut Leipzig (31 May 2001). "In memoriam Jürgen Moser". Moser Symposium, by MPI Leipzig. Retrieved 2013-11-16.
External links
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