P-spectrum and collapsing of connected sums, calculus of the limit

TL;DR

This paper investigates the behavior of the spectrum of the Hodge-Laplace operator during the collapse of a connected sum, providing new insights into the conformal spectrum on differential forms.

Contribution

It introduces methods to compute the limit spectrum under collapse, advancing understanding of spectral behavior in geometric analysis.

Findings

Derived the limit spectrum for collapsing connected sums.

Established new results on the conformal spectrum on differential forms.

Provided techniques for analyzing spectral limits in geometric degenerations.

Abstract

The goal of the paper is to calculate the limit sectrum of the Hodge-Laplace operator under the perturbation of collapse of one part of a connected sum. This gives some new results concerning the 'conformal spectrum' on differential forms.