5 papers · 1 filter
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…
On the Hessian Conjecture in Lorentzian Signature: Constant Pivots and Hesse Systems
Hanwen Liu
As a close relative of the Jacobian conjecture, the Hessian conjecture in dimension states that the local Legendre transform of a polynomial solution to the Monge--Ampère equat…
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 -tensors with Hermitian forms on the vector bundle of chiral 2-for…
A Self-Dual Frame Formalism of the SO(3) Yang-Mills Theory
Hanwen Liu
For a closed oriented Riemannian -manifold , we consider connections on the bundle of self-dual -forms. On the open locus where the self-d…
On Conservative Statistical Riemann Surfaces
Hanwen Liu
We establish a correspondence between information geometry and gauge theory. First, we define an important class of statistical manifolds, that is normalized and satisfies a conser…