Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Deformations of normal vector fields and the generalized Minkowski problem


Author: Herman Gluck
Journal: Bull. Amer. Math. Soc. 77 (1971), 1106-1110
MSC (1970): Primary 53C45, 53C20, 57D25; Secondary 57D50
DOI: https://doi.org/10.1090/S0002-9904-1971-12885-9
MathSciNet review: 0284955
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. A. D. Alexandrov, Zur Theorie gemischter Volumina konvexer Körper. I, II, III, Mat. Sb. 2 (1937), 947-972; 2 (1937), 1205-1238; 3 (1938).
  • 2. A. D. Alexandrov, Von der Flächenfunktion eines konvexen Körpers, Mat. Sb. 6 (48) (1939), 167.
  • 3. A. D. Alexandrov, Smoothness of the convex surface of bounded Gaussian curvature. C. R. (Dokl.) Acad. Sci. URSS 36 (1942), 195-199. MR 4, 69. MR 7626
  • 4. M. Berger, On Riemannian structures of prescribed Gauss curvature for compact two-dimensional manifolds, J. Diff. Geometry 5 (1971) (to appear). MR 295261
  • 5. W. Blaschke, Vorlesungen über differential Geometrie, Berlin, 1930; reprint, Chelsea, New York, 1967.
  • 6. T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Julius Springer, Berlin, 1934. MR 344997
  • 7. H. Busemann, Convex surfaces, Interscience Tracts in Pure and Appl. Math., no. 6, Interscience, New York, 1958. MR 21 #3900. MR 105155
  • 8. S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton Univ. Press, Princeton, N. J., 1952. MR 14, 398. MR 50886
  • 9. H. Gluck, The generalized Minkowski problem in differential geometry in the large, Ann. of Math, (to appear). MR 309021
  • 10. H. Gluck, The converse to the Four Vertex Theorem, l'Enseignement Math. (to appear). MR 344998
  • 11. J. Kazdan and F. Warner, Integrability conditions for $\Delta u=k-Ke\sp{\alpha u}$ with applications to Riemannian geometry, Bull. Amer. Math. Soc. 77 (1971), 819-823. MR 282314
  • 12. H. Lewy, On the existence of a closed surface realizing a given Riemannian metric, Proc. Nat. Acad. Sci. U.S.A. 24 (1938), 104-106.
  • 13. H. Minkowski, Allgemeine Lehrsätze über konvexer Polyeder, Nachr. Ges. Wiss. Göttingen 1897, 198-219.
  • 14. H. Minkowski, Volumen und Oberfläche, Math. Ann. 57 (1903), 447-495. MR 1511220
  • 15. J. Moser (to appear).
  • 16. L. Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953), 337-394. MR 15, 347. MR 58265
  • 17. A. V. Pogorelov, Regularity of a convex surface with given Gaussian curvature, Mat. Sb. 31 (73) (1952), 88-103. (Russian) MR 14, 679. MR 52807

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 53C45, 53C20, 57D25, 57D50

Retrieve articles in all journals with MSC (1970): 53C45, 53C20, 57D25, 57D50


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1971-12885-9

American Mathematical Society