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A CR Analogue of Yau’s Conjecture on Pseudoharmonic Functions of Polynomial Growth

  • Der-Chen Chang (a1) (a2), Shu-Cheng Chang (a3), Yingbo Han (a4) and Jingzhi Tie (a5)

In this paper, we first derive the CR volume doubling property, CR Sobolev inequality, and the mean value inequality. We then apply them to prove the CR analogue of Yau’s conjecture on the space consisting of all pseudoharmonic functions of polynomial growth of degree at most $d$ in a complete noncompact pseudohermitian $(2n+1)$ -manifold. As a by-product, we obtain the CR analogue of the volume growth estimate and the Gromov precompactness theorem.

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Author D.-C. C. is partially supported by an NSF grant DMS-1408839 and a McDevitt Endowment Fund at Georgetown University. Author S.-C. C. is partially supported by the MOST of Taiwan. (Corresponding author) Y. H. is partially supported by an NSFC grant 11201400, Nanhu Scholars Program for Young Scholars of Xinyang Normal University and the Universities Young Teachers Program of Henan Province (2016GGJS-096).

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Canadian Journal of Mathematics
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