Geometric Analysis Working Seminar

Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo

“Analytic Techniques for the Yamabe Problem : Part 1”

We will try to give a general overview of the method of the proof of the Yamabe Problem and the analytic preliminaries for the techniques used in the proof by Yamabe, Trudinger, Aubin and Schoen. We will start by giving a brief introduction to Sobolev Spaces. This will be followed Gagliardo-Nirenberg-Sobolev Inequality, Sobolev Embedding Theorems for compact Riemannian Manifold, 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 manifold. Finally we will explain local and global elliptic regularity and maximum principles. We will try to give proofs of as many results as possible. No familiarity with Sobolev Spaces is assumed.

MC 5479

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