Hanwen Liu

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20202026

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math.DG2026

Non-Kähler Critical Hermitian Metrics of the Dinew--Popovici Functional

Hanwen Liu

The Dinew--Popovici functional is an energy functional for Hermitian symplectic metrics in a fixed Aeppli cohomology class. Its vanishing characterizes the Kähler metrics in that c…

math.DG2026

A Note on the Rainich Problem for SU(2) Gauge

Hanwen Liu

We provide a resolution to the non-Abelian Rainich problem. By canonically identifying traceless symmetric $(0, 2)$ -tensors with Hermitian forms on the vector bundle of chiral 2-for…

math.DG2026

A Self-Dual Frame Formalism of the SO(3) Yang-Mills Theory

Hanwen Liu

For a closed oriented Riemannian $4$ -manifold $(M, g)$ , we consider $SO (3)$ connections on the bundle $Λ^{+}$ of self-dual $2$ -forms. On the open locus where the self-d…