## Asian Journal of Mathematics

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

#### Abstract

In this paper, we first obtain a CR version of Yau’s gradient estimate for eigenfunctions 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.

#### Article information

Source
Asian J. Math., Volume 18, Number 5 (2014), 929-946.

Dates
First available in Project Euclid: 2 December 2014

https://projecteuclid.org/euclid.ajm/1417489247

Mathematical Reviews number (MathSciNet)
MR3287008

Zentralblatt MATH identifier
1307.32015

#### Citation

Fan, Yen-Wen; Kuo, Ting-Jung. On the estimate of the first positive eigenvalue of a sublaplacian in a pseudohermitian manifold. Asian J. Math. 18 (2014), no. 5, 929--946. https://projecteuclid.org/euclid.ajm/1417489247