Koutroufiotis, Dimitri On a conjectured characterization of the sphere. (English) Zbl 0257.53056 Math. Ann. 205, 211-217 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 5 Documents MSC: 53A05 Surfaces in Euclidean and related spaces 53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov) 52A15 Convex sets in \(3\) dimensions (including convex surfaces) PDFBibTeX XMLCite \textit{D. Koutroufiotis}, Math. Ann. 205, 211--217 (1973; Zbl 0257.53056) Full Text: DOI EuDML References: [1] Alexandroff, A. D.: Les theorèmes d’unicité pour les surfaces fermées. Comptes Rendus (Doklady) de l’Académie des Sciences de l’URSS, vol. XXII, no. 3, 99-102 (1939). [2] Bianchi, L.: Vorlesungen über Differentialgeometrie. Teubner-Verlag 1910. · JFM 41.0676.01 [3] Chern, S. S.: Some new characterizations of the euclidean sphere. Duke Math. J.12, 279-290 (1945). · Zbl 0063.00833 [4] Hartman, P., Nirenberg, L.: On spherical image maps whose Jacobians do not change sign. Amer. J. Math.81, 901-920 (1959). · Zbl 0094.16303 [5] Hopf, E.: On Bernstein’s theorem on surfacesz(x, y) of nonpositive curvature. Proc. Amer. Math. Soc.1, 80-85 (1950). · Zbl 0039.16901 [6] Münzner, H. F.: Über eine spezielle Klasse von Nabelpunkten und analoge Singularitäten in der zentroaffinen Flächentheorie. Comm. Math. Helv.41, 88-104 (1966/67). · Zbl 0152.38902 [7] Nirenberg, L.: The Weyl and Minkowski problems in differential geometry in the large. Comm. Pure Appl. Math.VI, 337-394 (1953). · Zbl 0051.12402 [8] Simon, U.: Kennzeichnungen von Sphären. Math. Annalen175, 81-88 (1968). · Zbl 0153.23101 [9] Stoker, J. J.: On the uniqueness theorems for the embedding of convex surfaces in three-dimensional space. Comm. Pure Appl. Math.III, 231-257 (1950). · Zbl 0038.33601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.