Geodesic
Convexity properties of Legendre transformations (variational methods in quantum field theory)
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 43-58 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that in scalar field theory Legendre transforms are convex functionals in variables that have the meaning of unconnected Green's functions. It follows, in particular, that a stationarity point of these functionals in an extremum. 
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A. N. Vasil'ev; A. K. Kazanskii. Convexity properties of Legendre transformations (variational methods in quantum field theory). Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 43-58. http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a2/

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