Geodesic
Estimate of the upper bound on the Gaussian curvature of certain surfaces with boundary
Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 113-120.

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In this article it is shown that if S is a complete, regular (of class $C^4$) surface with geodesic boundary along which the normal curvature does not change sign, then the Gaussian curvature of the surface satisfies the condition: $\sup\limits_SK\ge0$. 
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     author = {L. I. Vorob'eva},
     title = {Estimate of the upper bound on the {Gaussian} curvature of certain surfaces with boundary},
     journal = {Matemati\v{c}eskie zametki},
     pages = {113--120},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a11/}
}
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L. I. Vorob'eva. Estimate of the upper bound on the Gaussian curvature of certain surfaces with boundary. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 113-120. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a11/