Steven G. Krantz
| Steven George Krantz | |
|---|---|
Steven G. Krantz in 2009
|
|
| Born |
February 3, 1951 San Francisco, California |
| Residence | U.S. |
| Institutions | UCLA, Penn State, Washington University in St. Louis |
| Alma mater | University of California at Santa Cruz, Princeton University |
| Doctoral advisor | Elias M. Stein, Joseph J. Kohn |
| Known for |
Complex analysis Harmonic analysis Partial differential equations Differential geometry Lie theory Geometric measure theory |
| Spouse |
Randi D. Ruden
married 1974–present |
Steven George Krantz (born February 3, 1951) is an American scholar, mathematician, and writer. He has authored numerous research papers and several books, and edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.
Steven Krantz grew up in Redwood City, California, just south of San Francisco. He graduated from Sequoia High School in 1967.
Krantz was an undergraduate at the University of California, Santa Cruz (UCSC), graduating in 1971. In the math department at UCSC his teachers included Nick Burgoyne, Marvin Greenberg, Ed Landesman, and Stan Philipp. Krantz graduated summa cum laude from UCSC.
Krantz obtained his PhD in mathematics from Princeton University in 1974 under the direction of Elias M. Stein and Joseph J. Kohn. Other influencers included Fred Almgren, Robert Gunning, and Ed Nelson.
Among Krantz's research interests are: several complex variables, harmonic analysis, partial differential equations, differential geometry, interpolation of operators, Lie theory, smoothness of functions, convexity theory, the corona problem, the inner functions problem, Fourier analysis, singular integrals, Lusin area integrals, Lipschitz spaces, finite difference operators, Hardy spaces, functions of bounded mean oscillation, geometric measure theory, sets of positive reach, the implicit function theorem, approximation theory, real analytic functions, analysis on the Heisenberg group, complex function theory, and real analysis. He applied wavelet analysis to plastic surgery, creating software for facial recognition. Krantz has also written software for the pharmaceutical industry.
Krantz has worked on the inhomogeneous Cauchy–Riemann equations (he obtained the first sharp estimates in a variety of nonisotropic norms), on separate smoothness of functions (most notably with hypotheses about smoothness along integral curves of vector fields), on analysis on the Heisenberg group and other nilpotent Lie groups, on harmonic analysis in several complex variables, on the function theory of several complex variables, on the harmonic analysis of several real variables, on partial differential equations, on complex geometry, on the automorphism groups of domains in complex space, and on the geometry of complex domains. He has worked with Siqi Fu, Robert E. Greene, Alexander Isaev and Kang-Tae Kim on the Bergman kernel, the Bergman metric, and automorphism groups of domains; with Song-Ying Li on the harmonic analysis of several complex variables; and with Marco Peloso on harmonic analysis, the inhomogeneous Cauchy–Riemann equations, Hodge theory, and the analysis of the worm domain. Krantz's book on the geometry of complex domains, written jointly with Robert E. Greene and Kang-Tae Kim, appeared in 2011.
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