Equivalence of Almgren-Pitts and phase-transition half-volume spectra

TL;DR

This paper proves the equivalence of two spectral theories for closed Riemannian manifolds, confirming a conjecture by Mazurowski and Zhou.

Contribution

It establishes the equality of Almgren-Pitts and phase-transition spectra, resolving a longstanding conjecture in geometric analysis.

Findings

Confirmed the conjecture of spectral equivalence.

Unified two major spectral theories in geometric analysis.

Provided a rigorous proof of the spectra's equality.

Abstract

We prove that the Almgren-Pitts and phase-transition half-volume spectra of a closed Riemannian manifold are equal. This confirms a conjecture of Liam Mazurowski and Xin Zhou.