On the CR Analogue of Reilly Formula and Yau Eigenvalue Conjecture
arXiv:1503.07639
Abstract
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.
22 pages. We generalize results to higher dimensional pseudohermitian manifolds. Some references are added