dg.differential geometry – Trends in Average Curvature Flow Research

It's been a few months since I'm curious about the average curvature flow and now I'm reading Robert Haslhofer's lecture notes. I love the subject and would like to research about it, but I do not know where to start or what are the current trends in research.

Can any one explain the main lines of research in this area, please?

Thanks in advance.