Weiyong He, University of Oregon

Title: Existence of Polyharmonic maps in the critical dimensions

Abstract: We discuss the existence of biharmonic maps and Polyharmonic maps in the critical dimensions.

The regularity of Polyharmonic maps was completely solved in 2009. Recently we made a step further to prove that given a null homotopy condition, there is always a Polyharmonic map in the critical dimensions for each free homotopy class [M, N].

We will also discuss some possible progress without a null homotopy condition.