Geodesic
CMC–surfaces, $\varphi$–geodesics and the Carathéodory conjecture
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2003), pp. 83-90 Cet article a éte moissonné depuis la source Math-Net.Ru

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A short proof of the Caratheodory conjecture about index of an isolated umbilic on the convex 2–dimensional sphere is suggested. 
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I. V. Nikolaev. CMC–surfaces, $\varphi$–geodesics and the Carathéodory conjecture. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2003), pp. 83-90. http://geodesic.mathdoc.fr/item/BASM_2003_1_a8/

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