Two principles of decoupling

TL;DR

This paper introduces two principles, radial and degeneracy locating, to advance the algebraic approach for decoupling problems across various manifolds, generalizing existing methods.

Contribution

It presents a novel algebraic framework with the radial and degeneracy locating principles to simplify decoupling problems for complex manifolds.

Findings

Generalizes the Pramanik-Seeger argument for the light cone

Reduces decoupling problems to non-degenerate or totally degenerate cases

Provides a new algebraic approach for decoupling across manifolds

Abstract

We put forward a radial principle and a degeneracy locating principle of decoupling. The former generalises the Pramanik-Seeger argument used in the proof of decoupling for the light cone. The latter locates the degenerate part of a manifold and effectively reduces the decoupling problem to two extremes: non-degenerate case and totally degenerate case. Both principles aim to provide a new algebraic approach of reducing decoupling for new manifolds to decoupling for known manifolds.