This is the web page for notes on the Spring 2003 graduate analysis seminar at UT, in which we are working our way as far as we can through Thierry Aubin's 1998 text, "Some Nonlinear Problems in Riemannian Geometry.''

A note on the affine connections and the gradient:  PS, PDF

A proof of the Sobolev embedding theorem for compact manifolds:  PS, PDF