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math.DG2024
RC-positivity, Schwarz's lemma and comparison theorems
Zhiyao Xiong, Xiaokui Yang, Shing-Tung Yau
It is well-known that the classical Schwarz lemma yields an explicit comparison of two Hermitian metrics with uniform constant negative curvature bounds through holomorphic maps be…
math.DG2024
Conjugate radius, volume comparison and rigidity
Zhiyao Xiong, Xiaokui Yang
In this paper, we prove conjugate radius estimate, volume comparison and rigidity theorems for Kähler manifolds with various curvature conditions.