Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
On the Ricci curvature of a compact Kähler manifold and the complex Monge- Ampère equation. I
5 Pith papers cite this work. Polarity classification is still indexing.
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Derives characteristic class formula for LVMB bundles over toric bases and establishes obstructions plus a new example for balanced metrics, with SKT characterization on LVM manifolds.
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.
Proves C^{1,1} regularity for a degenerate fully nonlinear equation on Hermitian manifolds with balanced metrics, yielding unique C^{1,1} solutions to the Donaldson equation.
Refined L^∞ lower (and conditional upper) bounds for Kähler-Einstein potentials on stable varieties near the non-klt locus via iterated logarithmic functions and explicit subsolutions/supersolutions to degenerate complex Monge-Ampère equations.
citing papers explorer
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A Levi-type decomposition on two-step solvable Lie algebras with a complex structure
Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
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Non-K\"ahler metrics on complex manifolds of LVMB type
Derives characteristic class formula for LVMB bundles over toric bases and establishes obstructions plus a new example for balanced metrics, with SKT characterization on LVM manifolds.
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The Sharp Edges of Calabi-Yau Manifolds: Designing Symmetric Models for Ricci-flat Metrics
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.
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Regularity of a Geodesic equation in the space of mixed Volume Forms on Hermitian Manifolds
Proves C^{1,1} regularity for a degenerate fully nonlinear equation on Hermitian manifolds with balanced metrics, yielding unique C^{1,1} solutions to the Donaldson equation.
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$L^\infty$-estimates of K\"ahler-Einstein potentials on stable varieties
Refined L^∞ lower (and conditional upper) bounds for Kähler-Einstein potentials on stable varieties near the non-klt locus via iterated logarithmic functions and explicit subsolutions/supersolutions to degenerate complex Monge-Ampère equations.