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Calabi-Yau fundamental groups are proven to be almost abelian, with ranks directly linked to cover irregularities.
Finite-time singularities in Kahler-Ricci flow exhibit controlled scalar curvature growth, paving the way for analytic minimal model program applications.
A direct proof of complex Hessian gradient estimates on Hermitian manifolds bypasses established complex analytic tools, revealing a new path via stability and comparison arguments.