CONCAVE DARBOUX THEOREM

We study the existence of a decomposition of a given germ of 1-form on an affine space as a linear combination with positive coefficients of the differentials of concave functions. The number of entries should be minimal. Necessary and sufficient conditions upon the form germ wit h regular degeneracy to have such a disaggregation are found. This pro blem originates from recent papers of P.A. Chiappori and I. Ekeland on the mathematical economy. (C) Academie des Sciences/Elsevier, Paris.