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On etudie les proprietes asymptotiques a t petit pour certaines equations de diffusion de la forme: (∂/∂t-Δ) ρ(y, x, t)=0, lim t→0 ρ(y, x, t)=S x (y), ou Δ est dans la classe des operateurs differentiels hypoelliptiques d'ordre 2 sur une variete connexe a m dimensions M

Off diagonal asymptotics of hypoelliptic diffusion equations and singular Riemannian geometry