On the renormalized volume of tubes over polarized K\"ahler-Einstein manifolds

TL;DR

This paper derives a formula for the renormalized volume of tubes over polarized Kähler-Einstein manifolds, linking it to the Einstein constant and polarization volume.

Contribution

It provides a new explicit formula connecting the renormalized volume with geometric invariants of polarized Kähler-Einstein manifolds.

Findings

Explicit formula for renormalized volume in terms of Einstein constant and polarization volume

Establishes a direct relationship between geometric invariants and tube volume

Advances understanding of volume calculations in Kähler geometry

Abstract

A formula of the renormalized volume of tubes over polalized K\"{a}hler-Einstein manifolds is given in terms of the Einstein constant and the volume of the polarization.