Yang's Kähler–Ricci-flow Lyapunov-exponent conjecture

From papers

Let (Mn,g)(M^n,g) be a complete noncompact Kähler manifold with nonnegative curvature and maximal volume growth. Let g(t)g(t), t[0,+)t\in[0,+\infty), be the unique complete solution of the Kähler–Ricci flow with initial metric gg supplied by the cited existence theorem. Denote by μi(p)\mu_i(p) the asymptotic exponents associated with this flow, and let dmin(i)d_{\operatorname{min}}^{(i)} be the components of the refined minimal-degree vector; let ASCD(M,g(t))\operatorname{ASCD}(M,g(t)) denote the average scalar-curvature decay. Yang's Kähler–Ricci-flow conjecture. For every 1in1\leq i\leq n, μi(p)\mu_i(p) is independent of pp, and

μi=dmin(i)1.\mu_i=d_{\operatorname{min}}^{(i)}-1.

Moreover, ASCD(M,g(t))\operatorname{ASCD}(M,g(t)) is invariant along the flow g(t)g(t). 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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