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Reilly, Robert C.

Geometric applications of the solvability of Neumann problems on a Riemannian manifold. (English) Zbl 0457.53008

Arch. Ration. Mech. Anal. 75, 23-29 (1980).
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Cited in 2 Reviews
Cited in 30 Documents

MSC:

53B20 Local Riemannian geometry

Keywords:

Ricci curvature; locally convex hypersurface; Laplace-Beltrami operator; Neumann problem; metric ball

Citations:

Zbl 0132.160; Zbl 0115.393
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Full Text: DOI

References:

[1] Aleksandrov, A. D., Uniqueness Theorems for Surfaces in the Large, V. American Math. Soc. Translations (2) 21 (1962), 412–416. MR27#698e. · Zbl 0119.16603
[2] Aleksandrov, A. D., A characteristic property of spheres. Ann. Mat. Pura Appl.(4) 58, 303–315 (1962), MR26 No. 722. · Zbl 0107.15603 · doi:10.1007/BF02413056
[3] Berger, M., Gauduchon, P., & E. Mazet, Le spectre d’une variété Riemannienne. Springer Lecture Notes 194, (1971). MR 43 No. 8025. · Zbl 0223.53034
[4] Bishop, R., & R. Crittenden, Geometry of manifolds. Pure and Applied Math., vol. XV. New York: Academic Press 1964. MR 29 No. 6401. · Zbl 0132.16003
[5] Bonnesen, T., & W. Fenchel, Konvexe Körper. New York: Chelsea Publishing Co., 1948.
[6] Eisenhart, L. P., Riemannian Geometry. Princeton: University Press 1925.
[7] Fiala, F., Le probléme des isopérimétres sur les surfaces ouvertes á courbure positive. Comm. Math. Helv. 13, 293–346 (1941), MR 3-301. · Zbl 0025.23003 · doi:10.1007/BF01378068
[8] Gallot, S., Équations différentielles caractéristiques de la sphére. Ann. Sci. Ec. Norm. Super. Ser IV 12, 235–267 (1979).
[9] Gray, A., The volume of a small geodesic ball of a Riemannian manifold. Michigan Math. J. 20, 329–344 (1973). MR 49 No. 3765. · Zbl 0279.58003
[10] Hörmander, L., Linear Partial Differential Operators. Berlin Heidelberg New York: Springer 1969. MR 40#1687. · Zbl 0175.39201
[11] Minkowski, H., Volumen und Oberfläche. Math. Ann. 57, 447–495 (1903). · JFM 34.0649.01 · doi:10.1007/BF01445180
[12] Obata, M., Certain conditions for a Riemannian manifold to be isometric with a sphere. J. Math. Soc. Japan 14, 333–340 (1962), MR 25 No. 5479. · Zbl 0115.39302 · doi:10.2969/jmsj/01430333
[13] Reilly, R., Applications of the Hessian operator in a Riemannian manifold. Indiana Univ. Math. J. 26, 459–472 (1977). · Zbl 0391.53019 · doi:10.1512/iumj.1977.26.26036
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