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A CR Analogue of Yau’s Conjecture on Pseudoharmonic Functions of Polynomial Growth
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 71 / Issue 6 / December 2019
- Published online by Cambridge University Press:
- 07 January 2019, pp. 1367-1394
- Print publication:
- December 2019
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- Article
- Export citation
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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.
