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<p> We give a proof in semi-group theory based on the Malliavin Calculus of Bismut type in semi-group theory and Wentzel-Freidlin estimates in semi-group of our result giving an expansion of an hypoelliptic heat-kernel outside the cut-locus where Bismut’s non-degeneray condition plays a preominent role. </p>

Estimate of an Hypoelliptic Heat-Kernel outside the Cut-Locus in Semi-Group Theory