All two-dimensional expanding Ricci solitons

The second author and H. Yin have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a nonatomic Radon measure as a conformal factor. This led to the discovery of a large array of new expanding Ricci solitons. In this paper we use the recent uniqueness theory in this context, also developed by the second author and H. Yin, to give a complete classification of all expanding Ricci solitons on surfaces. Along the way, we prove a converse to the existence theory: every complete Ricci flow on a surface over a time interval $(0,T)$ admits a $t\downarrow 0$ limit within the class of admissible initial data.Comment: Better notation in several parts for v2. Theorems and proofs remain the sam