Eigenvalue Estimate for the basic Laplacian on manifolds with foliated   boundary, part II
  In [4], we gave a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic $1$-forms defined on a compact manifold whose boundary is endowed with a Riemannian flow. In this paper, we extend this result to the case of the first eigenvalue on basic $p$-forms for $p>1$. As in [4], the limiting case allows to characterize the manifold $\mathbb{R} \times B' / \Gamma$ for some group $\Gamma$, and where $B'$ denotes the unit closed ball. In particular, we describe the Riemannian product $\mathbb{S}^1\times \mathbb{S}^n$ as the boundary of a manifold. 
Fida El Chami, George Habib, Ola Makhoul and Roger Nakad
math.DG