I. Existence for the Canham problem involves constructing a comparison surface of each genus g with W less than 8π and arbitrarily small isoperimetric ratio v by gluing g+1 small catenoidal bridges to the bigraph of a singular solution to the linearized Willmore equation ∆(∆+2)φ = 0 on the (g+1)-punctured sphere S^2 (joint with Peter McGrath).

II. More evidence for the conjecture that the Lawson surfaces with W less than 8π solve the Willmore problem: they are all W-stable, and they also minimize W among all surfaces with the same symmetries and genus (joint with Peng Wang and Ying Lü).