On the First eigenvalue of the Laplace operator for Compact Spacelike submanifolds in Lorentz-Minkowski Spacetime ${\mathbb{L}}^m$

Francisco J. Palomo, Alfonso Romero

By means of a family of counter-examples, it is shown that the Reilly upper bound for the first eigenvalue of the Laplace operator for a compact submanifold in Euclidean space does…