Geodesic
A CR Analogue of Yau’s Conjecture on Pseudoharmonic Functions of Polynomial Growth
Canadian journal of mathematics, Tome 71 (2019) no. 6, pp. 1367-1394

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DOI

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.
DOI : 10.4153/CJM-2018-024-3
Mots-clés : CR Bochner formula, heat kernel, subgradient estimate, Liouvile theorem, CR volume doubling property, CR Sobolev inequality, mean value inequality 
Chang, Der-Chen; Chang, Shu-Cheng; Han, Yingbo; Tie, Jingzhi. A CR Analogue of Yau’s Conjecture on Pseudoharmonic Functions of Polynomial Growth. Canadian journal of mathematics, Tome 71 (2019) no. 6, pp. 1367-1394. doi: 10.4153/CJM-2018-024-3
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     author = {Chang, Der-Chen and Chang, Shu-Cheng and Han, Yingbo and Tie, Jingzhi},
     title = {A {CR} {Analogue} of {Yau{\textquoteright}s} {Conjecture} on {Pseudoharmonic} {Functions} of {Polynomial} {Growth}},
     journal = {Canadian journal of mathematics},
     pages = {1367--1394},
     year = {2019},
     volume = {71},
     number = {6},
     doi = {10.4153/CJM-2018-024-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-024-3/}
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