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It is well known that for a sequence of metrics in a fixed conformal class with constant scalar curvature on a manifold with dimension 3 (see [4] for further reference) or higher (see [2] for further reference), the blowingup set must be finite and simple (each bubbling point carry exactly one sphere). The corresponding statement in dimension 2 is widely expected to hold. The author learned this problem from a joint paper of YanYan Li and Tai Shafrir [3] when he studied a different but related problem [5], [6]. The purpose of this paper is to construct an example of a sequence of metrics in a unit disk with constant curvature 1 and uniformly bounded area which develops branch bubbles at the center of the disk, thereby providing an counter example to the analogous statements in dimension two. Interested readers are referred to [3] for detailed history of this problem and further references. Very briefly, Brezis and Merle [1] studied a sequence of solutions {^n} in an open unit disk Bi satisfying the equation:

Remarks on the existence of branch bubbles on the blowup analysis of equation $- \Delta u = e^{2u}$ in dimension two