We consider the heat flow of pseudoharmonic maps from a closed pseudohermitian manifold (M2n+1,J,θθ) into a compact Riemannian manifold (Nm,g). In our previous work, we proved the global existence of the solution for the pseudoharmonic map heat flow, provided the sectional curvature of the target manifold N is nonpositive. In this talk, we show that the solution of the pseudoharmonic map heat flow blows up in finite time if the initial map belongs to a nontrivial homotopy class and its initial energy is sufficiently small.

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