An infinite dimensional balanced embedding problem III: Asymptotics near infinity

TL;DR

This paper advances the understanding of the asymptotic behavior of the logarithmic balanced model metric near infinity, confirming parts of a previous conjecture through refined analytical tools.

Contribution

It introduces refined methods to analyze the asymptotics of the balanced metric, partially confirming a prior conjecture about its behavior at infinity.

Findings

Partial confirmation of the conjecture on asymptotics near infinity

Development of refined analytical tools for the balanced metric

Improved understanding of the metric's behavior at large scales

Abstract

We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our previous work on the asymptotic behavior of the balanced metric near infinity.