Conjugate radius, volume comparison and rigidity

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arxiv 2408.02080 v1 pith:XWTOI43B submitted 2024-08-04 math.DG

Zhiyao Xiong , Xiaokui Yang This is my paper · ORCID

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keywords comparisonconjugateradiusrigidityvolumeahlerconditionscurvature

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In this paper, we prove conjugate radius estimate, volume comparison and rigidity theorems for K\"ahler manifolds with various curvature conditions.

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First eigenvalue estimates on complete K\"ahler manifolds
math.DG 2025-07 conditional novelty 7.0 of 10

On complete Kähler manifolds with HSC ≥ 2, the first eigenvalue of the Laplacian is at least (320n+256)/(81n+63), which tends to 320/81 as n grows.
RC-positivity, Schwarz's lemma and comparison theorems
math.DG 2024-12 conditional novelty 6.0 of 10

Under weak pointwise curvature comparison (RC-positivity), the pullback metric is dominated, giving diameter, volume, and rigidity theorems.