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

DOI: https://dx.doi.org/10.4310/AJM.2014.v18.n5.a7

Authors

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)

Abstract

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.

Keywords

CR gradient estimate, CR diameter, eigenvalue estimate, sublaplacian

2010 Mathematics Subject Classification

Primary 32V05, 32V20. Secondary 53C56.

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Published 25 November 2014