Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo
“Analytic Techniques for the Yamabe Problem : Part 2”
We will continue our discussion of Sobolev Spaces. This will be followed Gagliardo- Nirenberg-Sobolev Inequality, Sobolev Embedding Theorems for compact Riemannian Man- ifold, Rellich-Kondrachov theorem and the General Sobolev Inequalities. We will also talk about a theorem due to Aubin about the Sobolev constant for any compact Riemannian man- ifold. Finally we will explain local and global elliptic regularity and maximum principles. We will try to give proofs of as many results as possible.
MC 5403