Year: 2025
Type: article
Abstract: Gromov used convex integration to prove that any closed orientable three-manifold equipped with a volume form admits three divergence-free vector fields which are linearly independent at every point. We provide an alternative proof of this using geometric properties of eigenspinors in three dimensions. In fact, our proof shows that for any Riemannian metric, one can find three divergence-free vector fields such that at every point they are orthogonal and have the same non-zero length.
Source: Documenta Mathematica
DOI: 10.4171/dm/989
Author: Francesco Lin
Institution: Columbia University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
OpenAlex ID: W4413583331