# The limit of the Hermitian-Yang-Mills flow on reflexive sheaves

## TL;DR

This paper investigates the long-term behavior of the Hermitian-Yang-Mills flow on reflexive sheaves, establishing a key isomorphism with the double dual of the associated graded sheaf, thus answering a significant open question.

## Contribution

It proves the asymptotic limit of the flow is isomorphic to the double dual of the graded sheaf from the Harder-Narasimhan-Seshadri filtration, clarifying the flow's limiting behavior.

## Key findings

- The limiting reflexive sheaf matches the double dual of the graded sheaf.
- The result confirms a conjecture by Bando and Siu.
- Provides a detailed analysis of the flow's asymptotics.

## Abstract

In this paper, we study the asymptotic behavior of the Hermitian-Yang-Mills flow on a reflexive sheaf. We prove that the limiting reflexive sheaf is isomorphic to the double dual of the graded sheaf associated to the Harder-Narasimhan-Seshadri filtration, this answers a question by Bando and Siu.