Halsey Royden

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Halsey Royden

Halsey Lawrence Royden | |
---|---|

Born | September 26, 1928 Phoenix, Arizona, U.S> |

Died | August 22, 1993 | (aged 64)

Other names | Royden, H. L. |

Occupation | Mathematician |

Academic background | |

Doctoral advisor | Lars Valerian Ahlfors |

**Halsey Lawrence Royden** Jr. (September 26, 1928 - August 22, 1993) was an American mathematician, specializing in complex analysis on Riemann surfaces, several complex variables, and complex differential geometry.^{[1]} Royden is the author of a popular textbook on Real Analysis.^{[2]}

After study at Phoenix College, Royden transferred in 1946 to Stanford University, where he received his bachelor's degree in 1948 and his master's degree in 1949, with a master's thesis written under the supervision of Donald Spencer. Royden received his Ph.D. in 1951 at Harvard University under the supervision of Lars Ahlfors with thesis *Harmonic functions on open Riemann surfaces*.^{[3]} At Stanford University he became an assistant professor in 1951, an associate professor in 1953, and a full professor in 1958. In addition to serving on the faculty of the mathematics department, for Stanford's School of Humanities and Sciences he was in 1962-1965 associate dean, in 1968-1969 executive dean (acting dean until the vacancy was resolved), and in 1973-1981 dean. In 1981 he resigned as dean to work full-time as a mathematics professor.^{[4]} He was on the editorial board of the Pacific Journal of Mathematics for the five years from 1956 to 1960. Royden was a Visiting Scholar at the Institute for Advanced Study in Princeton for 3 months in the fall of 1969, 3 months in the spring of 1974, and for the academic year 1982-1983.^{[5]}

In 1970, he showed the equivalence of the Kobayashi metric and the Teichmüller metric on Teichmüller space.^{[6]}

Royden was a Guggenheim Fellow for the academic year 1973-1974.^{[7]} In 1974 he was an Invited Speaker (*Intrinsic metrics on Teichmüller space*) at the International Mathematical Congress in Vancouver.

Upon his death he was survived by his wife (the mathematician Virginia "Jinx" Voegeli), two daughters (one, Leigh Royden, a noted geologist), a son, and several grandchildren.^{[1]} His doctoral students include Alan Huckleberry, Peter A. Loeb and John Wetzel.

- Royden, H. L. (November 1949). "The Coefficient Problem for Bounded Schlicht Functions".
*Proc Natl Acad Sci U S A*.**35**(11): 657-662. Bibcode:1949PNAS...35..657R. doi:10.1073/pnas.35.11.657. PMC 1063103. PMID 16578322. - with P. R. Garabedian: Garabedian, P. R.; Royden, H. L. (January 1952). "A Remark on Cavitation Flow".
*Proc Natl Acad Sci U S A*.**38**(1): 57-61. Bibcode:1952PNAS...38...57G. doi:10.1073/pnas.38.1.57. PMC 1063498. PMID 16589052. - Royden, H. L. (1952). "Harmonic functions on open Riemann surfaces".
*Trans. Amer. Math. Soc*.**73**: 40-94. doi:10.1090/s0002-9947-1952-0049396-8. MR 0049396. - Royden, H. L. (1952). "On the regularity of boundary points in potential theory".
*Proc. Amer. Math. Soc*.**3**: 82-86. doi:10.1090/s0002-9939-1952-0048639-x. MR 0048639. - Royden, H. L. (1953). "Some counterexamples in the classification of open Riemann surfaces".
*Proc. Amer. Math. Soc*.**4**(3): 363-370. doi:10.1090/s0002-9939-1953-0054056-x. MR 0054056. - Royden, H. L. (1954). "The conformal rigidity of certain subdomains on a Riemann surface".
*Trans. Amer. Math. Soc*.**76**: 14-25. doi:10.1090/s0002-9947-1954-0059377-8. MR 0059377. - Royden, H. L. (1954). "A property of quasi-conformal mapping".
*Proc. Amer. Math. Soc*.**5**(2): 266-269. doi:10.1090/s0002-9939-1954-0060598-4. MR 0060598. - Royden, H. L. (1956). "Rings of analytic and meromorphic functions".
*Trans. Amer. Math. Soc*.**83**(2): 269-276. doi:10.1090/s0002-9947-1956-0089908-5. MR 0089908. - Royden, H. L. (1958). "Rings of meromorphic functions".
*Proc. Amer. Math. Soc*.**9**(6): 959-965. doi:10.1090/s0002-9939-1958-0103974-7. MR 0103974. - Royden, H. L. (1963). "Function algebras".
*Bull. Amer. Math. Soc*.**69**(3): 281-298. doi:10.1090/s0002-9904-1963-10900-3. MR 0149327. *Real Analysis*. Macmillan. 1963.*2nd edition*. 1968.*3rd edition*. 1988.*4th edition*. 2010.- Royden, H. L. (1974). "The extension of regular holomorphic maps".
*Proc. Amer. Math. Soc*.**43**(2): 306-310. doi:10.1090/S0002-9939-1974-0335851-X. MR 0335851. - Royden, H. L. (1974). "Holomorphic fiber bundles with hyperbolic fiber".
*Proc. Amer. Math. Soc*.**43**(2): 311-312. doi:10.1090/S0002-9939-1974-0338465-0. MR 0338465. - Royden, H. L. (1984). "The Picard theorem for Riemann surfaces".
*Proc. Amer. Math. Soc*.**90**(4): 571-574. doi:10.1090/S0002-9939-1984-0733408-6. MR 0733408. *A History of Mathematics at Stanford*in*A century of mathematics in America*, American Mathematical Society, 1989, vol. 2.

- ^
^{a}^{b}"Former dean and mathematician Halsey Royden dead at 64, Stanford News Service, 8/24/93". news.stanford.edu. Retrieved . **^**Royden, H. L. (1963).*Real Analysis*. Macmillan.*2nd edition*. 1968.*3rd edition*. 1988.*4th edition*. 2010.**^**Halsey Royden at the Mathematics Genealogy Project**^**"Memorial Resolution, Halsey L. Royden (1928-1993), Stanford Historical Society" (PDF). histsoc.stanford.edu. Archived from the original (PDF) on 2011-07-27. Retrieved .**^**"Royden, Halsey L. | Institute for Advanced Study". ias.edu. Retrieved .**^**Royden, H. L. (March 1970). "Report on the Teichmüller Metric*"**.*Proc Natl Acad Sci USA*.***65**(3): 497-499. Bibcode:1970PNAS...65..497R. doi:10.1073/pnas.65.3.497. PMC 282934. PMID 16591819.**^**"Guggenheim Awards: 16 Receive Fellowships".*The Stanford Daily*.**163**(38). 17 April 1973.

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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