Asian Journal of Mathematics

Volume 18 (2014)

Number 5

On the estimate of first positive eigenvalue of a sublaplacian in a pseudohermitian manifold

Pages: 929 – 946



Yen-Wen Fan (Department of Mathematics, National Taiwan University, Taipei, Taiwan)

Ting-Jung Kuo (Taida Institute For Mathematical Sciences (TIMS), National Taiwan University, Taipei, Taiwan)


In this paper, we first obtain a CR version of Yau’s gradient estimate for eigenfunc- tions of a sublaplacian. Second, by using CR analogue of Li-Yau’s eigenvalue estimate, we are able to obtain a lower bound of the first positive eigenvalue in a pseudohermitian manifold of nonvanishing pseudohermitian torsion and nonpositive lower bound on pseudohermitian Ricci curvature.


CR gradient estimate, CR diameter, eigenvalue estimate, sublaplacian

2010 Mathematics Subject Classification

Primary 32V05, 32V20. Secondary 53C56.

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