  The global existence of solutions to the relativistic Vlasov-Maxwell system
given sufficiently regular finite energy initial data is a longstanding open
problem. The main result of Glassey-Strauss (1986) shows that a solution $(f,
E, B)$ remains $C^1$ as long as the momentum support of $f$ remains bounded.
Alternate proofs were later given by Bouchut-Golse-Pallard (2003) and
Klainerman-Staffilani (2002). We show that only the boundedness of the momentum
support of $f$ after projecting to any two dimensional plane is needed for $(f,
E, B)$ to remain $C^1$.
