Inner Contact Billiards

Construct a natural inner contact billiard theory and determine what geometric structure its reflection dynamics should preserve.

Background

The paper develops only an outer billiard construction. It proposes a candidate inner reflection law in projective contact three-space, but does not determine whether that law is natural or what invariant structure an appropriate inner theory should possess.

References

Is there a natural inner contact billiard? What kind of structure should these preserve?

Outer Contact Billiards  (2608.19393 - Caliz et al., 19 Aug 2026) in Section 6, “Open questions,” item 2

What is an appropriate analogue of Theorem \ref{thm:ContTransf} to decide which reflection law shall earn the name of inner contact billiards?

Outer Contact Billiards  (2608.19393 - Caliz et al., 19 Aug 2026) in Section 6, “Open questions,” item 2