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We present a description of singular horizontal curves of a totallynonholonomic analytic distribution in term of the projections of the orbits ofsome isotropic subanalytic singular distribution defined on the nonzeroannihilator of the initial distribution in the cotangent bundle. As aby-product of our first result, we obtain, under an additional assumption onthe constructed subanalytic singular distribution, a proof of the minimal rankSard conjecture in the analytic case. It establishes that from a given pointthe set of points accessible through singular horizontal curves of minimalrank, which corresponds to the rank of the distribution, has Lebesgue measurezero.

Abnormal subanalytic distributions and minimal rank Sard Conjecture