Presented by: 
Huy Nguyen, UQ
Tue 27 Nov, 3:00 pm - 4:00 pm
Room T103, Building 50
We consider surfaces conformally immersed in R^3 with L^2 bounds on the norm of the second fundamental form. In particular, we will study the Liouville equation for such surfaces and give an extension of the Classical Gauss-Bonnet formula for surfaces and study its behaviour under conformal transformations of Euclidean space.
We will then classify certain limit cases of these bounds, for example we will suitably generalise Osserman's classification of complete non-compact minimal surfaces with total curvature equal to 8 Pi to the case of complete non-compact surfaces with total bounded curvature.