2 problems

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Li–Jia's Bernstein conjecture for the Abreu equation
Li–Jia's conjecture. Then $f$ must be a quadratic polynomial. This is a Bernstein property for the Abreu equation on an entire strictly convex potential; the source attributes the…
Conjectureopenabreu-equation bernstein-problem monge-ampere-equationsarXiv posted 2 days ago
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Uniform stability conjecture for the toric Abreu equation
Let $\Delta$ be a Delzant polytope, let $K\in C^\infty(\overline{\Delta})$ , and let $\mathcal L_K$ be the linear functional defining relative K-stability. The pair $(\Delta,K)$ is…
Conjectureopenabreu-equation k-stability toric-geometryarXiv posted 2 days ago

Li–Jia's Bernstein conjecture for the Abreu equation