Under what necessary and sufficient condition on $r > 0$ does there exist $u$ belonging to $\mathrm { SL } \left( \mathbb { R } ^ { 2 m } \right)$ such that $u \left( B ^ { 2 m } ( 1 ) \right) \subset B ^ { 2 m } ( r )$?
Under what necessary and sufficient condition on $r > 0$ does there exist $u$ belonging to $\mathrm { SL } \left( \mathbb { R } ^ { 2 m } \right)$ such that $u \left( B ^ { 2 m } ( 1 ) \right) \subset B ^ { 2 m } ( r )$?