We study a family of geometric variational functionals introduced by Hamilton, and considered later Daskalopulos, Sesum, Del Pino Hsu, in order to understand the behavior maximal solutions Ricci flow both compact noncompact complete Riemannian manifolds finite volume. The case dimension two has some peculiarities, which force us use different ideas from corresponding higher-dimensional case. Un...

A widely used theorem of analysis asserts that a uniformly bounded, equicontinuous family of functions has a compact closure in the space of continuous functions. This lemma, variously attributed to Arzela, Escoli, Montel, Vitali, and so on, is of importance in the theory of integral equations, conformal mapping, calculus of variations, and so on. In recent years the lemma has been generalized ...