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.