K\"ahler tori with almost non-negative scalar curvature

TL;DR

This paper investigates Kähler metrics with nearly non-negative scalar curvature on complex tori, demonstrating that such metrics converge to flat tori under certain conditions, thus contributing to the understanding of geometric stability.

Contribution

It proves convergence of non-collapsing sequences of Kähler metrics with almost non-negative scalar curvature to flat tori, advancing the torus stability problem.

Findings

Sequences of Kähler metrics with almost non-negative scalar curvature converge to flat tori.

The convergence is weak and occurs after passing to a subsequence.

The work supports the stability conjecture for complex tori.

Abstract

Motivated by the torus stability problem, in this work we study K\"ahler metrics with almost non-negative scalar curvature on complex torus. We prove that after passing to a subsequence, non-collapsing sequence of K\"ahler metrics with almost non-negative scalar curvature will converge to flat torus weakly.