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Konvexe Mengen in Riemannschen Mannigfaltigkeiten. (German) Zbl 0369.52006


MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
53C20 Global Riemannian geometry, including pinching
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References:

[1] Aleksandrov, A.D.: Über das fast überall existierende Differential einer konvexen Funktion und gewisse damit zusammenhängende Eigenschaften konvexer Flächen. Leningrad. Gos. Univ. U?en. Zap. Ser. Mat. Nauk6, 3-35 (1939)
[2] Anderson, R.D., Klee, V.L., Jr.: Convex functions and upper semi-continuous collections. Duke Math. Z.19, 349-357 (1952) · Zbl 0047.15702
[3] Bangert, V.: Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten. J. reine angew. Math. (erscheint) · Zbl 0396.52007
[4] Bangert, V.: Über die Approximation von lokal konvexen Mengen. Manuscripta Math. (erscheint) · Zbl 0392.53027
[5] Bangert, V.: On the monotony of the boundary volumes of geodesically convex sets. Preprint
[6] Bangert, V.: Riemannsche Mannigfaltigkeiten mit nicht-konstanter konvexer Funktion. Arch. Math. (erscheint) · Zbl 0372.53021
[7] Bishop, R.L.: Infinitesimal convexity implies local convexity. Indiana Univ. Math. J.24, 169-172 (1974/75) · Zbl 0289.53026
[8] Bishop, R.L., O’Neill, B.: Manifolds of negative curvature. Trans. Amer. Math. Soc.145, 1-49 (1969) · Zbl 0191.52002
[9] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. of Math.96, 413-443 (1972) · Zbl 0246.53049
[10] Favard, J.: Sur les corps convexes. J. Math. Pures Appl.12, 219-282 (1933) · JFM 59.0710.01
[11] Federer, H.: Geometric measure theory. Grundlehren der mathematischen Wissenschaften, Bd. 153. Berlin-Heidelberg-New York: Springer 1969 · Zbl 0176.00801
[12] Greene, R.E., Wu, H.: Integrals of subharmonic functions on manifolds of nonnegative curvature. Invent. Math.27, 265-298 (1974) · Zbl 0342.31003
[13] Greene, R.E., Wu, H.:C ? convex functions and manifolds of positive curvature. Acta Math.137, 209-245 (1976) · Zbl 0372.53019
[14] Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. Lecture Notes in Mathematics 55. Berlin-Heidelberg-New York: Springer 1968 · Zbl 0155.30701
[15] Gromoll, D., Meyer, W.: On complete open manifolds of positive curvature. Ann. of Math.90, 75-90 (1969) · Zbl 0191.19904
[16] Karcher, H.: Schnittort und konvexe Mengen in vollständigen Riemannschen Mannigfaltigkeiten. Math. Ann.177, 105-121 (1968) · Zbl 0157.28801
[17] Kelley, J.: General topology. New York-Toronto-London: van Nostrand 1955 · Zbl 0066.16604
[18] McMullen, P.: On the inner parallel body of a convex body. Israel J. Math.19, 217-219 (1974) · Zbl 0307.52004
[19] Rinow, W.: Die innere Geometrie der metrischen Räume: Grundlehren der mathematischen Wissenschaften, Bd. 105, Berlin-Göttingen-Heidelberg: Springer 1961 · Zbl 0096.16302
[20] Walter, R.: On the metric projection onto convex sets in Riemannian spaces. Arch. Math. (Basel)25, 91-98 (1974) · Zbl 0311.53054
[21] Walter, R.: A generalized Allendoerfer-Weil formula and an inequality of the Cohn-Vossen type. J. Differential Geometry10, 167-180 (1975) · Zbl 0308.53042
[22] Walter, R.: Some analytical properties of geodesically convex sets. Abh. Math. Sem. Univ. Hamburg45, 263-282 (1976) · Zbl 0332.53026
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