We thank Dimitris Politis and Mohsen Pourahmadi for sharing their work and thoughts. The constructive comments of the four Referees and the Associate Editor is gratefully acknowledged. We thank the Editor for his encouragement to submit a revision.

Preuve du théorème 1.2.

In this section, we prove our main theorem (Theorem 1.22) characterizing solutions of the Ricci flow.

Throughout this section uε is a nonzero weak solution of \rm div(A(x/ε)∇uε)=0 in B2 for some A∈A(λ,M). In view of Theorem 3.3 we assume that uε satisfies the doubling condition,

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