The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are $C^3$-close to round, but without assuming

Ricci flow is a powerful technique using a heat-type equation to deform Riemannian metrics on manifolds to better metrics in the search for geometric decomposit

In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They

The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove globa