Eigenvalue estimates for submanifolds of warped product spaces

Abstract

We give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type $N^n \times_f Q^q$, where $f \in C^\infty(N)$. We also study the essential spectrum of these minimal submanifolds.Comment: 17 page

Isoperimetric inequalities and monotonicity formulas for submanifolds in warped products manifolds

“…These manifolds were first introduced by R. Bishop and B. O'Neill in 1969, see [2], and has had increasing importance due its applications as model spaces in general relativity. There are many interesting papers in this subject, see for example [12], [3], [6], [4], [1], [18], [19], [8], and [5] for more references and results.…”