Homogeneous Solutions of Pluriclosed Flow on Closed Complex Surfaces

TL;DR

This paper classifies the long-term behavior of homogeneous solutions to the pluriclosed flow on various closed complex surfaces and constructs new expanding soliton solutions on their universal covers.

Contribution

It provides a comprehensive classification of homogeneous solutions and introduces new expanding soliton solutions for the pluriclosed flow.

Findings

Classification of long-time behavior on multiple surface types

Construction of new expanding soliton solutions

Insights into pluriclosed flow dynamics on complex surfaces

Abstract

Streets and Tian introduced a parabolic flow of pluriclosed metrics. We classify the long time behavior of homogeneous solutions of this flow on closed complex surfaces including minimal Hopf, Inoue, Kodaira, and non-Kahler, properly elliptic surfaces. We also construct expanding soliton solutions to the flow on the universal covers of these surfaces by taking blowdown limits of these homogeneous solutions.