# Stecklov operator vs Laplacian operator

There's one paper published at siggraph that captured my attention : Steklov Spectral Geometry.

I'm not an expert in geometry processing, but I'm trying to learn as much as I can. You can easily read in the introduction:

In this paper we provide a practical and mathematically justified spectral approach to extrinsics geometry for geometry processing via an extrinsic alternative to the intrinsic Laplace-Beltrami operator.

I read through the paper and, for who like me enjoy signal processing, is a very nice read. It my understanding the operator they propose an alternative of the classic laplace beltrami operator:

$$\Delta_{\mathcal{S}} \psi(x) = 0$$

The operator proposed is

$$\left\{ \begin{array}{ll} \Delta \psi(x) = 0 & x \in \Omega \\ \nabla_n \psi(x) = \lambda \psi(x) & x \in \Gamma \end{array} \right.$$

Which is the "Steklov eigenproblem". The first line of the system above is the laplace equation again (but volumetric) the second line is a condition on the normal derivative.

What I don't understand is why does the former operator represent an "intrinsics" operator while the latter represent an extrinsic operator.