Uniqueness theorems for some open and closed surfaces in three-space

J. J. Stoker

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1978)

  • Volume: 5, Issue: 4, page 657-677
  • ISSN: 0391-173X

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Stoker, J. J.. "Uniqueness theorems for some open and closed surfaces in three-space." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.4 (1978): 657-677. <http://eudml.org/doc/83797>.

@article{Stoker1978,
author = {Stoker, J. J.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Uniqueness Theorems; Surfaces in Three-Space; Christoffel's Problem; Minkowski's Problem; Weyl's Problem; Global Space; Liebmann's Problem},
language = {eng},
number = {4},
pages = {657-677},
publisher = {Scuola normale superiore},
title = {Uniqueness theorems for some open and closed surfaces in three-space},
url = {http://eudml.org/doc/83797},
volume = {5},
year = {1978},
}

TY - JOUR
AU - Stoker, J. J.
TI - Uniqueness theorems for some open and closed surfaces in three-space
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1978
PB - Scuola normale superiore
VL - 5
IS - 4
SP - 657
EP - 677
LA - eng
KW - Uniqueness Theorems; Surfaces in Three-Space; Christoffel's Problem; Minkowski's Problem; Weyl's Problem; Global Space; Liebmann's Problem
UR - http://eudml.org/doc/83797
ER -

References

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  1. [1] N.V. Efimov, Flächenverbiegung im Grossen (translation from Russian), Akademie-Verlag, Berlin (1957). MR85569
  2. [2] C.C. Hsiung, A uniqueness theorem for Minkowski's problem for convex surfaces with boundary, Illinois J. Math. (1958). Zbl0083.37301MR96286
  3. [3] E. Kann, A new method for infinitesimal rigidity of surfaces with K &lt; 0, J. Differential Geometry (1970). Zbl0194.52503MR259817
  4. [4] E. Kann, An elementary proof of a finite rigidity problem by infinitesimal rigidity methods, Proc. Amer. Math. Soc. (1976). Zbl0338.53038MR420518
  5. [5] H. Lewy, On differential geometry in the large (Minkowski's problem), Trans. Amer. Math. Soc. (1938). Zbl0018.17403JFM64.0714.03
  6. [6] V.I. Oliker, The uniqueness of the solution in Christoffel and Minkowski problems for open surfaces (1973), translation from Russian by Consultant's Bureau, NewYork (1975). 
  7. [7] A.V. Pogorelov, Extrinsic geometry of convex surfaces (translation from Russian), Amer. Math. Soc., Providence (1973). Zbl0311.53067MR346714
  8. [8] F. Rellich, Zur ersten Randwertaufgabe bei Monge-Ampèreschen Differentialgleichungen vom Elliptischen Typus; differentialgeometrische Anwendungen, Math. Ann., 107 (1932). Zbl0005.35501JFM58.0498.01
  9. [9] J.J. Stoker, On the uniqueness theorems for the embedding of convex surfaces in three-dimensional space, Comm. Pure Appl. Math. (1950). Zbl0038.33601MR40025
  10. [10] J.J. Stoker, Open convex surfaces which are rigid, Courant Anniversary Volume, Interscience, New York (1948). Zbl0033.01803MR22689
  11. [11] J.J. Stoker, Differential geometry, Wiley-Interscience, NewYork (1969). Zbl0182.54601MR240727
  12. [12] M. Tsuji, Uniqueness theorems for surfaces of positive and negative curvature, Diss. N.Y.U. (1968). 
  13. [13] V.A. Volkov - V.I. Oliker, Uniqueness of the solution of Christoffel's problem for nonclosed surfaces (1969), translated from Russian by Consultant's Bureau, New York (1971). 
  14. [14] K. Voss, Differentialgeometrie geschlossener Flächen im Euklidischen Raum. I, Jahresber. D. Math. Ver. (1960). Zbl0096.36602MR126813
  15. [15] H. Weyl, Über die Starrheir der Eiflächen und konvexen Polyeder, Sitzungsberichte der Preussischen Akademie der Wissenschaften (1917). Zbl46.1115.02JFM46.1115.02

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