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• W2963955448 abstract "This paper mainly focuses on the CR analogue of the three-circle theorem in a complete noncompact pseudohermitian manifold of vanishing torsion being odd dimensional counterpart of Kähler geometry. In this paper, we show that the CR three-circle theorem holds if its pseudohermitian sectional curvature is nonnegative. As an application, we confirm the first CR Yau’s uniformization conjecture and obtain the CR analogue of the sharp dimension estimate for CR holomorphic functions of polynomial growth and its rigidity when the pseudohermitian sectional curvature is nonnegative. This is also the first step toward second and third CR Yau’s uniformization conjecture. Moreover, in the course of the proof of the CR three-circle theorem, we derive CR sub-Laplacian comparison theorem. Then Liouville theorem holds for positive pseudoharmonic functions in a complete noncompact pseudohermitian $$(2n+1)$$ -manifold of vanishing torsion and nonnegative pseudohermitian Ricci curvature." @default.
• W2963955448 created "2019-07-30" @default.
• W2963955448 creator A5021203511 @default.
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• W2963955448 date "2019-05-22" @default.
• W2963955448 modified "2023-10-14" @default.
• W2963955448 title "On the three-circle theorem and its applications in Sasakian manifolds" @default.
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• W2963955448 doi "https://doi.org/10.1007/s00526-019-1538-8" @default.
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