Examining Non-Compact Ambient Obstruction Solitons
Abstract: We will discuss a new program of studying ambient obstruction solitons using a geometric flow for a general tensor q. We begin by establishing a number of results for solitons to the q-flow. Examining both the compact and non-compact cases, we ascribe properties to q allowing us to prove that certain solitons are q-flat. Specifically, we will consider a number of regularity conditions on X that enable the use maximum principle type arguments. Finally, we apply these results to the ambient obstruction flow, the Bach flow (n ≥ 5), and the Cotton flow demonstrating the utility of this approach.