Constructing soliton solutions of geometric flows by separation of variables

Abstract

This note surveys and compares results on the separation of variables construction for soliton solutions of curvature equations including the K\"ahler-Ricci flow and the Lagrangian mean curvature flow. In the last section, we propose some new generalizations in the Lagrangian mean curvature flow case.Comment: Contribution to Special Issue(s) in the Bulletin of Institute of Mathematics, Academia Sinica (N.S.