Controlling the energy flow on the materials surface is analogous to adding a curve to the surface in a fourth spatial dimension. It’d be Like curving a flat plane in a third dimension to control the flow of water on the surface.
I am sure you are visualizing something sensible but reading that, to me, felt as ambiguous as the article.
Can you use a specific example with an actual physical 3D + extra dimension situation?
For instance, an actual example of a 4D-to-3D situation is the mapping of 3D space + 1D time to a 3D RGB color space, when representing the visual experience of a flying formation of LED drones.
Something that concrete?
you could come up with some material that naturaly has those kinds of properties without being wavy. but mathematically its the same thing.