Proves existence, uniqueness and flow convergence for weak solutions of generalized Monge-Ampère and supercritical dHYM equations on boundary cohomology classes via viscosity and pluripotential techniques.
The Critical LYZ Equation in K\"ahler Geometry
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abstract
We establish the existence of smooth solutions for the LYZ equation at the critical phase $\theta =(n-2)\frac{\pi}{2}$, thereby solving the critical case of a problem posed by Collins-Jacob-Yau and Li concerning the solvability for phase $\theta \leq (n-2)\frac{\pi}{2}$. As applications, we solve the 3D Hessian equation $\sigma_2 = 1$ and the 4D Hessian quotient equation $\sigma_3 = \sigma_1$ under weaker assumptions than previously required.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Weak solutions of the generalized Monge-Amp\`ere equation and the supercritical deformed Hermitian-Yang-Mills equation: boundary cases
Proves existence, uniqueness and flow convergence for weak solutions of generalized Monge-Ampère and supercritical dHYM equations on boundary cohomology classes via viscosity and pluripotential techniques.