On gradient Kähler Ricci shrinkers the dimension of polynomial-growth holomorphic functions and (p,0)-forms is finite, with sharp linear-growth estimates and power bounds under curvature assumptions.
Cao, Recent progress on Ricci solitons, Recent advances in geometric analysis, 1--38, Adv
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The dimension of polynomial growth holomorphic functions and forms on gradient K\"ahler Ricci shrinkers
On gradient Kähler Ricci shrinkers the dimension of polynomial-growth holomorphic functions and (p,0)-forms is finite, with sharp linear-growth estimates and power bounds under curvature assumptions.