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Sup-slopes and sub-solutions for fully nonlinear elliptic equations

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arxiv 2405.03074 v1 pith:B5TNUULW submitted 2024-05-05 math.AP math.DG

Bin Guo , Jian Song This is my paper · ORCID
classification math.APmath.DG
keywords equationsconditionellipticfullyhermitianhessianmanifoldsnonlinear
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abstract

We establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on closed Riemannian or hermitian manifolds, including both hessian and hessian quotient equations. It settles an open problem of Li and Urbas. Such a condition is based on an analytic slope invariant analogous to the slope stability and the Nakai-Moishezon criterion in complex geometry. As an application, we solve the non-constant $J$-equation on both hermitian manifolds and singular K\"ahler spaces.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Datar-Mete-Song minimal slope conjecture

    math.AG 2026-08 conditional novelty 7.0 of 10

    The paper proves the Datar-Mete-Song conjecture: a pair of Kähler classes is semi-stable exactly when its minimal J-slope equals the topological J-slope.

  2. The twisted constant in Calabi-Yau type equation

    math.AP 2025-06 conditional novelty 6.0 of 10

    A necessary and sufficient solvability criterion is extended to almost Hermitian manifolds with gradient terms, yielding explicit infimum formulas for the twisted constants in Calabi-Yau type equations.

  3. A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds

    math.AP 2025-06 conditional novelty 5.0 of 10

    Existence of solutions for fully nonlinear elliptic equations on compact almost Hermitian manifolds is established under a sub-slope condition, with applications to the Hessian quotient and deformed Hermitian-Yang-Mil...

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