Multilinear Evolution Equations for Time-Harmonic Flows

TL;DR

This paper introduces a multilinear framework for describing time-harmonic hypersurface flows in conformally flat manifolds, revealing integrable structures and conserved quantities, with invariance under conformal transformations.

Contribution

It develops a novel multilinear description of hypersurface motions that generates integrable matrix equations and conserved quantities, independent of conformal factor changes.

Findings

Generation of infinitely many conserved quantities.

Derivation of new integrable matrix equations.

Invariance of the description under conformal transformations.

Abstract

It is shown that time-harmonic hypersurface motions in various, conformally flat, N-dimensional manifolds admit a multilinear description, dL/dt={ L, M_1, ... , M_{N-2} }, automatically generating infinitely many conserved quantities, as well as leading to new (integrable) matrix equations. Interestingly, the conformal factor can be changed without changing L.