Characterizations via linear combinations of curvature measures

Archiv der Mathematik

Volumn 70, Issue 3, 1998, Pages 250-256

  Kohlmann, Peter ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032221128     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000130050192     Document Type: Article

References (25)

1. A. D. ALEXANDROW, Uniqueness theorems for surfaces in the large. I-V, Vestnik. Leningrad. Univ. Fiz. Khim 11, 5-17 (1956); 12, 15-44 (1957); 13, 14-26 (1958); 13, 27-34 (1985); 13, 5-8 (1958). Amer. Math. Soc. Transl. Ser. 2 21, 341-416 (1962).
2. A. D. ALEXANDROW, Uniqueness theorems for surfaces in the large. I-V, Vestnik. Leningrad. Univ. Fiz. Khim 11, 5-17 (1956); 12, 15-44 (1957); 13, 14-26 (1958); 13, 27-34 (1985); 13, 5-8 (1958). Amer. Math. Soc. Transl. Ser. 2 21, 341-416 (1962).
3. A. D. ALEXANDROW, Uniqueness theorems for surfaces in the large. I-V, Vestnik. Leningrad. Univ. Fiz. Khim 11, 5-17 (1956); 12, 15-44 (1957); 13, 14-26 (1958); 13, 27-34 (1985); 13, 5-8 (1958). Amer. Math. Soc. Transl. Ser. 2 21, 341-416 (1962).
4. A. D. ALEXANDROW, Uniqueness theorems for surfaces in the large. I-V, Vestnik. Leningrad. Univ. Fiz. Khim 11, 5-17 (1956); 12, 15-44 (1957); 13, 14-26 (1958); 13, 27-34 (1985); 13, 5-8 (1958). Amer. Math. Soc. Transl. Ser. 2 21, 341-416 (1962).
5. A. D. ALEXANDROW, Uniqueness theorems for surfaces in the large. I-V, Vestnik. Leningrad. Univ. Fiz. Khim 11, 5-17 (1956); 12, 15-44 (1957); 13, 14-26 (1958); 13, 27-34 (1985); 13, 5-8 (1958). Amer. Math. Soc. Transl. Ser. 2 21, 341-416 (1962).
6. A. D. ALEXANDROW, Uniqueness theorems for surfaces in the large. I-V, Vestnik. Leningrad. Univ. Fiz. Khim 11, 5-17 (1956); 12, 15-44 (1957); 13, 14-26 (1958); 13, 27-34 (1985); 13, 5-8 (1958). Amer. Math. Soc. Transl. Ser. 2 21, 341-416 (1962).
7. P. S. BULLEN, D. S. MITRINOVIC and P. M. VASIC, Means and Their Inequalities. Math. Appl. 31. Dordrecht 1988.
8. K. ECKER and G. HUISKEN, Immersed hypersurfaces with constant Weingarten curvature. Math. Ann. 283, No. 2, 329-332 (1989).
9. H. FEDERER, Curvature measures. Trans. Amer. Math. Soc. 93, 418-491 (1959).
10. H. FEDERER, Geometric Measure Theory. Grundlehren Math. Wiss. 153. Berlin-Heidelberg-New York 1969.
11. E. HEINTZE and H. KARCHER, A general comparison theorem with applications to volume estimates for submanifolds. Ann. Sci. École Norm. Sup. (4) 11, 451-470 (1978).
12. P. KOHLMANN, Curvature measures and Steiner formulae in space forms. Geom. Dedicata 40, No. 2, 191-211 (1991).
13. P. KOHLMANN, Minkowski integral formulas for compact convex bodies in standard space forms. Math. Nachr. 166, 217-228 (1994).
14. A. LI, Some theorems on Codazzi tensors and their applications to hypersurfaces in Riemannian manifold of constant curvature. Geom. Dedicata 23, 103-113 (1987).
15. S. MONTIEL and A. ROS, Compact hypersurfaces: The Alexandrov theorem for higher order mean curvatures, Differential geometry. Pitman Monogr. Surveys Pure Appl. Math. 52, 279-296 (1991).
16. J. R. SANGWINE-YAGER, A representation for volume involving interior reach. Math. Ann. 298, 1-5 (1994).
17. R. SCHNEIDER, Curvature measures of convex bodies. Ann. Mat. Pura Appl. (4) 116, 101-134 (1978).
18. R. SCHNEIDER, Boundary structure and curvature of convex bodies. In: Contributions to geometry, J. Toelke and J. M. Wills, eds., 13-59. Siegen 1978 (1979).
19. R. SCHNEIDER, Bestimmung konvexer Mengen durch Krümmungsmaße. Comment. Math. Helv. 54, 42-60 (1979).
20. R. SCHNEIDER, Convex bodies: The Brunn-Minkowski theory. Encyclopedia Math. Appl. 44. Cambridge 1993.
21. U. SIMON, Minkowskische Integralformeln und ihre Anwendungen in der Differentialgeometrie im Großen. Math. Ann. 173, 307-321 (1967).
22. U. SIMON, Kennzeichnungen von Sphären. Math. Ann. 175, 81-88 (1968).
23. n+1. Tôhoku Math. J. 31, 202-209 (1929).
24. K. VOSS, Einige differentialgeometrische Kongruenzsätze für geschlossene Flächen und Hyperflächen. Math. Ann. 131, 180-218 (1956).
25. M. ZÄHLE, Integral and current representation of Federer's curvature measures. Arch. Math. (Basel) 46, 557-567 (1986).