Donald C. Spencer
(19122001)
a Honorary Member of the Diffiety Institute

Personal data
Born: Boulder, Colorsdo,USA April 25, 1912
Married to Mary J. Halley July 25, 1936
Children: Maredith, Marianne
Married 2nd to Natalie Robertson Sanborn July 7, 1951
Child: Donald Clayton

Education
B.A., University of Colorado, 1934
B.S., Massachusetts Institute of Technology, 1936
Ph. D., Cambridge University, England, 1939
Sc. D., Cambridge University, England, 1963

Professional Experience
Instructor, Massachusetts Institute of Technology, 1939-1942
Associate Professor, Stanford University, 1942-1946
Member of Applied Mathematics Group, New York University, 1944-1945
Professor, Stanford University, 1946-1950, 1963-1968
Associate Professor, Princeton University, 1950-1953
Professor, Princeton University, 1953-1963, 1968-1978
Eugene Higgins Professor of Mathematics, Princeton University, 1971-1972
Henry Burchard Fine Professor of Mathematics, Princeton University, 1972-1978
Henry Burchard Fine Professor of Mathematics, emeritus,, Princeton University, 1978-

Honors and distinctions
Sc.D. honoris causa, Purdue University, 1971
Scott visiting professor of mathematics, University of Pensilvania, Fall, 1964
Fulbright grant for study and lecturing, Colle`ge de France, 1954-1955
Joint recipient with A.C. Schaeffer of the Bocher Memorial Prize, American Mathematical Society, 1948
Phi Beta Kappa, University of Colorado, 1933

Other Relevant Information
Member of National Academy of Sciences, USA, 1961-
Fellow of American Academy of Arts and Sciences, USA, 1967-
Member of Editorial Board, Proceedings of the National Academy of Sciences, USA, 1965-1967
Member of Editorial Board, Annals of Mathematics, 1958-1962
Member of Editorial Board, Transactions of the American Mathematical Society, 1950-1955
Member of Editorial Board, American Journal of Mathematics, 1967-1975
Member of Editorial Board, Journal of Differential Geometry, 1967-1981
Colloquium Lecturer, American Mathematical Society, Summer meeting of 1968
Lecturer, VIII S'eminaire de Math'ematiques Sup'erieures, University of Montreal
Visiting Committee, Department of Mathematics, Massachusetts Institute of Technology, Alumnus Member, 1968-1969
Co-editor (with S. Iyanaga), Global Analysis: Paper in honor of K. Kodaira, University of Tokio Press and Princeton University Press

Here you can find papers by Joseph J. Kohn, Phillip A. Griffiths, Hubert Goldschmidt, Enrico Bombieri, Bohous Cenkl, Paul Garabedian, and Louis Nirenberg consecrated to the memory of Professor D. C. Spencer.

List of Ph.D. Students of Donald C. Spencer

Bibliography of the publications of D. C. Spencer

I. Books and Monographs

  1. (with A. C. Schaeffer). Coefficient Regions for Schlicht Functions, Amer. Math. Soc. Colloq. Publ., Vol. 35, New York, 1950, 311 pp.
  2. (with M.Schiffer). Functionals of Finite Riemann Surfaces, Princeton University Press, 1954, 451 pp.
  3. (with H. K. Nickerson and N. E. Steenrod). Advanced Calculus, Van Nostrand, Princeton, New Jersey, 1959, 540 pp.
  4. (with A. Kumpera). Lie Equations. Volume I: General Theory, Annals of Math. Studies, No. 73, Princeton University Press, 1972, 293 pp.

II. Papers

    1939

  1. On a Hardy-Littlewood problem of diophantine approximation, Proc. Cambridge Philos. Soc. 35 (1939) 527-547.

    1940

  2. On finitely mean valent functions. II, Tram. Amer. Math. Soc. 48 (1940) 418-435.
  3. On an inequality of Grunsky, Proc. Nat. AweL Sci. U.S.A. 26 (1940) 616-621.
  4. Note on some function-theoretic identities, J. London Math. Soc. 15 (1940) 84-86.

    1941

  5. On finitely mean valent functions, Proc. London Math. Soc. (2) 47 (1941) 201-211.
  6. On a theorem of Rengels, J. Math. Phys., Massachusetts fast. Tech. 20 (1941) 118-123.
  7. On distortion in analytic transformations, J. Math. Phys., Massachusetts Inst.Tech. 20 (1941)124-126.
  8. On mean one-valent functions, Ann. of Math. 42 (1941) 614-633.
  9. Distortion in Conformal Mapping (mimeographed), Additional note to lectures on conformal mapping of multiply-connected domains by S. Bergman, Brown University, 1941, 11 pp.

    1942

  10. The lattice points of tetrahedra, J. Math, Phys., Massachusetts Inst. Tech. 21 (1942) 189-197.
  11. (with R. Salem). The influence of gaps on density of integers, Duke Math. J. 9 (1942) 855-872.
  12. (with R. Salem). On sets of integers which contain no three terms in arithmetical progression, Proc. Nat. Acad. Sci. U.S.A. 28 (1942) 561-563.
  13. Note on mean one-valent functions, J. Math. Phys., Massachusetts Inst. Tech. 21 (1942) 178-188.
  14. Some remarks concerning the coefficients of schlicht functions, J. Math. Phys., Massachusetts Inst. Tech. 21 (1942) 63-68.
  15. (with S. Bergman). On distortion in pseudo-conformal mapping, Tram. Amer. Math. Soc. 51 (1942) 133-163.
  16. (with S. Bergman). A property of pseudo-conformal transformations in the neighborhood of boundary points. Duke Math. J. 9 (1942) 757-762.

    1943

  17. A function-theoretic identity, Amer. J. Math. 65 (1943) 147-160.
  18. (with A. C. Schaeffer). The coefficients of schlicht functions, Duke Math. J. 10 (1943) 611-635.

    1945

  19. (with A. C. Schaeffer). The coefficients of schlicht functions. II, Duke Math. J. 12 (1945) 107-125.
  20. (with M. Shiftman). The Force of Impact on a Sphere Striking a Water Surface: Approximation by the Flow about a Lens, 47 pp.; Second Approximation, 83 pp.. Applied Math. Panel, National Defense Research Committee, 1945 (Applied Mathematics Group, New York University, Report Nos. 105 and 133).

    1946

  21. (with A. C. Schaeffer). The coefficients of schlicht functions. III, Proc. Nat. Acad. Sci. U.S.A. 32 (1946) 111-115.

    1947

  22. (with A. C. Schaeffer). A general class of problems in conformal mapping, Proc. Nat. Acad. Sci. U.S.A. 33 (1947) 185-189.
  23. Some problems in conformal mapping, Bull. Amer. Math. Soc. 53 (1947) 417-439.
  24. (with A. C. Schaeffer). A variational method in conformal mapping, Duke Math. J. 14 (1947) 949-966.
  25. (with M. Shiftman). The flow of an ideal incompressible fluid about a lens. Quart. Appi. Math. 5 (1947) 270-288.

    1949

  26. (with A. C. Schaeffer). The coefficients of schlicht functions. IV, Proc. Nat. Acad. Sci. U.S.A. 35 (1949) 143-150.
  27. (with A. C. Schaeffer and M. Schiffer). The coefficient regions of schlicht functions, Duke Math. J. 16 (1949) 493-527.

    1950

  28. (with R. Salem). On sets which do not contain a given number of terms in arithmetical progression, Nieuw Arch. Wisk. (2) 13 (1950) 133-143.
  29. (with M. Schiffer) The coefficient problem for multiply-connected domains, Ann. of Math. 52 (1950) 362-402.
  30. (with A. C. Schaeffer). Models illustrating the third coefficient region for schlicht functions, Scripta Math. 16 (1950) 67 - 71.

    1951

  31. (with J.A.Jenkms). Hyperelliptic trajectories, Ann. of Math. 53 (1951) 4-35.
  32. (with M. Schiffer), A variational calculus for Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A I, No. 93, 1951, 9 pp.
  33. (with M. Schiffer). On the conformal mapping of one Riemann surface into another, Ann. Acad. Sci. Fenn. Ser. A I, No. 94, 1951, 10 pp.
  34. (with G. F. D.Duff). Harmonic tensors on manifolds with boundary, Proc. Nat. Acad. Sci. U.S.A. 37 (1951) 614-619.
  35. (with M. Schiffman). The force of impact on a cone striking a water surface (vertical entry), Comm. Pure Appl. Math. 4 (1951) 379-417.

    1952

  36. (with A. C. Schaeffer). Coefficient regions for schlicht functions, Proc. Internal. Congress Math. (Cambridge, U.S.A., 1950), Amer. Math. Soc., Vol. 11, 1952, 224-232.
  37. (with A. C. Schaeffer). A variational method for simply-connected domains, Construction and applications of conformal maps, Proc. Sympos., Nat. Bureau of Standards, Applied Math. Ser. No. 18, 1952, 189-191.
  38. (with M. Schiffer). Some remarks on variational methods applicable to multiply-connected domains. Construction and applications of conformal maps, Proc. Sympos., Nat. Bureau of Standards, Applied Math. Ser. No. 18, 1952, 193-198.
  39. (with G. F. D. Duff). Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math. 56 (1952) 128-156.
  40. (with P. R. Garabedian). Complex boundary value problems, Trans. Amer. Math. Soc. 73 (1952) 223-242.
  41. A generalization of a theorem of Hodge, Proc. Nat. Acad. Sci. U.S.A. 38 (1952) 533-534.
  42. Cauchy's formula on Kahler manifolds, Proc. Nat. Acad. Sci. U.S.A. 38 (1952) 76-80.
  43. (with P. R. Garabedian). Extremal methods in cavitational flow, J. Rational Mech. Anal. 1 (1952) 359-409.

    1953

  44. (with P. R. Garabedian). A complex tensor calculus for Kahler manifolds, Acta Math. 89 (1953) 279-331.
  45. Heat conduction on arbitrary Riemannian manifolds, Proc. Nat. Aca. Sci U.S.A. 39 (1953) 327-330.
  46. Real and complex operators on manifolds, Contributions to the theory of Riemann surfaces, Annals of Math. Studies, No. 30, Princeton University Press, 1953, 203-227.
  47. Cohomology and the Riemann-Roch theorem, Proc. Nat. Acad. Sci. U.S.A. 39 (1953) 660-669.
  48. (with K. Kodaira). On arithmetic genera of algebraic varieties, Proc. Nat. Acad. Sci. U.S.A. 39 (1953) 641 -649.
  49. (with K. Kodaira). Groups of complex line bundles over compact Kahler varieties, Proc. Nat. Acad. Sci. U.S.A. 39 (1953) 868-872.
  50. (with K. Kodaira). Divisor class groups on algebraic varieties, Proc. Nat. Acad. Sci. U.S.A. 39 (1953) 872-877.
  51. (with K. Kodaira). On a theorem of Lefschetz and the lemma of Enriques-Severi-Zariski, Proc. Nat. Acad. Sci. U.S.A. 39 (1953) 1273-1278.

    1954

  52. Dirichlet's principle on manifolds, Studies in Math. and Mech. presented to Richard von Mises, Academic Press, New York, 1954, 127-134.

    1955

  53. Potential theory and almost-complex manifolds, Lectures on functions of a complex variable. University of Michigan Press, 1955, 15-43.

    1956

  54. (with V.K.A.M. Gugenheim). Chain homotopy and the de Rham theory, Proc. Amer. Math. Soc. 7 (1956) 144-152.

    1957

  55. (with J. J. Kohn). Complex Neumann problems, Ann. of Math. 66 (1957) 89-140.
  56. (with K. Kodaira). On the variation of almost-complex structure, Algebraic Geometry and Topology, Princeton University Press, 1957, 139-150.

    1958

  57. A spectral resolution of complex structure, Sympos. Internac. Topologia Algebraica Mexico, 1958, 68-76.
  58. (with K. Kodaira). On deformations of complex analytic structures. I, II, Ann. of Math. 67 (1958) 328-466.
  59. (with K. Kodaira and L. Nirenberg). On the existence of deformations of complex analytic structures, Ann. of Math. 68 (1958) 450-459.
  60. (with K. Kodaira). A theorem of completeness for complex analytic fibre spaces, Acta Math. 100 (1958) 281 -294.

    1959

  61. (with K. Kodaira). Existence of complex structure on a differentiable family of deformations of compact complex manifolds, Ann. of Math. 70 (1959) 145-166.
  62. (with K. Kodaira). A theorem of completeness of characteristic systems of complete continuous systems, Amer. J. Math. 81 (1959) 477-500.

    1960

  63. Some remarks on perturbation of structure, Analytic Functions, Princeton University Press, 1960, 67-87.
  64. (with K. Kodaira). On deformations of complex analytic structures. III. Stability theorems for complex structures, Ann. of Math. 71 (1960) 43-76.
  65. (with L. Nirenberg). On rigidity of holomorphic imbeddings, Contributions to function theory (Internal. Colloq. Function Theory) Tata Institute, Bombay, 1960, 133-137.

    1961

  66. (with K. Kodaira). Multifoliate structures, Ann. of Math. 74 (1961) 52-100.
  67. Some remarks on homological analysis and structures, Differential Geometry, (Proc. Sympos. Pure Math. Vol. 3, Tucson, Arizona, 1960), Amer. Math. Soc., 1961, 56-86.
  68. Deformation of pseudogroup structures, Proc. Nat. Acad. Sci. U.S.A. 47 (1961) 1205-1208.
  69. Complex analysis, article in the 1961 printing of the Encyclopaedia Britannica (listed under ANALYSIS, COMPLEX), 7 pp.
  70. A type of formal exterior differentiation associated with psedogroups, Scripta Math. 26 (1961) 101-106.

    1962

  71. Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I, II, Ann. of Math. 76 (1962) 306-445.
  72. Instrinsic formulation of the equation of structure of a transitive continuous pseudogroup, Studies in Math. Anal. and Related Topics, Stanford University Press, 1962, 373-376.

    1963

  73. Harmonic integrals and Neumann problems associated with linear partial differential equations. Outlines of the joint Soviet-American Sympos. on Partial Differential Equations, August, 1963, Novosibirsk (Moscow, 1963) 253-260.

    1964

  74. De Rham theorems and Neumann decompositions associated with linear partial differential equations, Ann. Inst. Fourier (Grenoble) 14 (1964) 1-20,
  75. Existence of local coordinates for structures defined by elliptic pseudo-groups, Differential Analysis (Papers presented at the Bombay Colloq. 1964), Oxford University Press, 1964, 135-162.

    1965

  76. Deformation of structures on manifolds defined by transitive, continuous pseudogroups, Part III: Structures defined by elliptic pseudogroups, Ann. of Math. 81 (1965) 389-450.
  77. Remark on formal exterior differentiation, J. Analyse Math. 14 (1965) 433-442.

    1966

  78. The theory of harmonic integrals, Some Recent Advances in the Basic Sciences, Vol. 1, Annual Sci. Conf. Proc. Belter Graduate School of Sci., Yeshiva University, New York, 1966, 137-155.
  79. Some remarks on overdetermined systems of linear partial differential equations, Proc. Katata Conf. on the theory of partial differential equations and on the theory of complex manifolds, Kyoto, 1966, 52-82.

    1969

  80. Overdetermined systems of linear partial differential equations. Bull. Amer.Math.Soc. 75 (1969) 179-239.
  81. On deformation of pseudogroup structures. Global Analysis (Papers in Honor of K. Kodaira), Princeton University Press, 1969, 367-395.

    1970

  82. Uncoupled overdetermined systems, Global Analysis (Proc. Sympos. Pure Math. Vol. 16, Berkeley, California, 1968), Amer. Math. Soc., 1970, 211-220.

    1971

  83. Overdetermined operators: Some remarks on symbols, Proc. Internal. Congress Math. (Nice, France, 1970). Gauthier-Villars, Paris, Vol. 2, 1971, 251-256.
  84. Flat differential operators, (Sympos. on Several Complex Variables, Park City, Utah, 1970), Lecture Notes in Math., Vol. 184, Springer, Berlin, 1971,85-108.

    1974

  85. (with A. Kumpera). Systems of Lineara Partial Differential Equations and Deformation of Pseudogroup Structures, Seminaire math. superieure, 1969, Presses Universite de Montreal, 1974, 100 pp.
  86. Curvatures associated with differential operators, (Geometric Differentielle Colloque Santiago de Compostella, Espagne, 1972), Lecture Notes in Math. Vol. 392, Springer, Berlin, 1974, 64-75.

    1975

  87. Construction of complexes for Lie equations, Manifolds-Tokyo 1973, University of Tokyo Press, 1975, 303-311.

    1976

  88. (with H. Goldschmidt). On the non-linear cohomology of Lie equations. I, Acta Math. 136 (1976) 103-170.
  89. (with H. Goldschmidt). On the non-linear cohomology of Lie equations. II, Acta Math. 136 (1976) 171-239.

    1977

  90. (with H. Goldschmidt). Submanifolds and over-determined differential operators. Complex Analysis and Algebraic Geometry (A collection of papers dedicated to K. Kodaira), Iwanami Shoten Publishers and Cambridge University Press, 1977, 319-356.

    1978

  91. (with H. Goldschmidt). On the non-linear cohomology of Lie equations. Ill, IV, J. Differential Geometry 13 (1978) 409-526.