Yang's Kähler–Ricci-flow Lyapunov-exponent conjecture
Yang's Kähler–Ricci-flow Lyapunov-exponent conjecture
Let be a complete noncompact Kähler manifold with nonnegative curvature and maximal volume growth. Let , , be the unique complete solution of the Kähler–Ricci flow with initial metric supplied by the cited existence theorem. Denote by the asymptotic exponents associated with this flow, and let be the components of the refined minimal-degree vector; let denote the average scalar-curvature decay. Yang's Kähler–Ricci-flow conjecture. For every , is independent of , and
Moreover, is invariant along the flow . The conjecture connects the Lyapunov-type asymptotics of the Kähler–Ricci flow with refined minimal degrees and curvature decay; the supplied text gives no resolution.
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Sources & referencesView supporting material
Primary source
Yuang Shi, “Minimal Degrees, Volume Growth, and Curvature Decay on Complete Kähler Manifolds”, arXiv:2511.01263 (2026).
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