Classification of solitons for pluriclosed flow on complex surfaces

Abstract

We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be K\"ahler except for the possibility of steady solitons on minimal Hopf surfaces. Then, we construct steady solitons on all class $1$ Hopf surfaces by exploiting a natural symmetry ansatz.