On the parabolic Donaldson's equation over a compact complex manifold

TL;DR

This paper proves the existence, uniqueness, and long-term convergence of smooth solutions to a parabolic Donaldson's equation on compact complex manifolds, advancing understanding of geometric flows in complex geometry.

Contribution

It establishes the long-time existence, uniqueness, and convergence of solutions to a new parabolic Donaldson's equation on compact complex manifolds.

Findings

Proved the uniqueness of solutions.

Established long-time existence of solutions.

Showed convergence to a smooth function as time approaches infinity.

Abstract

We prove the uniqueness and long time existence of the smooth solution to a parabolic Donaldson's equation on a compact complex manifold $M$.Then we show that a suitably normalized solution converges to a smooth function on $M$ in $C^\infty$ topology as $t\rightarrow\infty$.