M'arcio Batista

Second Eigenvalue Estimates and Spectral Rigidity for Submanifolds of Compact Rank-One Symmetric Spaces

In this paper, we establish upper bounds for the second eigenvalue of the Schr\"odinger operator $L=\Delta+|\sigma|^2+k$ on $k$-dimensional closed submanifolds of the compact projective spaces $\mathbb F P^m$, where $\mathbb F\in\{\mathbb R,\mathbb C,\mathbb H\}$, as well as the Cayley projective plane. The estimates a...