Asian Journal of Mathematics
Volume 22 (2018)
On the CR analogue of Reilly formula and Yau eigenvalue conjecture
Pages: 919 – 940
In this paper, we derive the CR Reilly’s formula and its applications to studying of the first eigenvalue estimate for CR Dirichlet eigenvalue problem and embedded $p$-minimal hypersurfaces. In particular, we obtain the first Dirichlet eigenvalue estimate in a compact pseudohermitian $(2n+1)$-manifold with boundary and the first eigenvalue estimate of the tangential sublaplacian on closed oriented embedded $p$-minimal hypersurfaces in a closed pseudohermitian $(2n+1)$-manifold of vanishing torsion.
pseudohermitian minimal surface, CR Dirichlet eigenvalue, CR Reilly formula, tangential sublaplacian, CR Yau eigenvalue conjecture
2010 Mathematics Subject Classification
53C56, 32V05, 32V20
Research supported in part by the MOST of Taiwan.
Received 5 September 2015
Accepted 25 November 2016
Published 9 November 2018