Year: 2026
Type: preprint
Abstract: A vanishing sequence $V_n$ of divergence-free matrix fields is one that is bounded in $L^1$ and is carried by open sets $A_n$ of vanishing volume. Recently established, Bouchitté's vanishing mass conjecture says that the directions such a sequence can carry are rigidly constrained: their limiting distribution must be a superposition of microstructures whose barycenters are singular matrices. We prove the converse in the non-symmetric setting: every such superposition is attained by a vanishing sequence. In fact, we are able to construct divergence-free fields $V_n$ $supported$ on $A_n$, whose relative boundary is a smooth compact manifold.
Source: arXiv (Cornell University)
Institutions: University of Pisa, University of Naples Federico II
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1792883159, G2971504390, G8097609347
OpenAlex ID: W7214052049