A parabolic Monge-Ampère type equation of Gauduchon metrics

Abstract

We prove the long time existence and uniqueness of solution to a parabolic Monge-Ampère type equation on compact Hermitian manifolds. We also show that the normalization of the solution converges to a smooth function in the smooth topology as $t$ approaches infinity which, up to scaling, is the solution to a Monge-Ampère type equation. This gives a parabolic proof of the Gauduchon conjecture based on the solution of Székelyhidi, Tosatti and Weinkove to this conjecture.

30 pages. Correct some typos, accepted by International Mathematics Research Notices (IMRN)

References in corpus (4)

• Gauduchon metrics with prescribed volume form
• Inoue surfaces and the Chern-Ricci flow
• The Chern-Ricci flow on Oeljeklaus-Toma manifolds
• The Chern-Ricci flow and holomorphic bisectional curvature

Cited by in corpus (1)

• Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications