How do two capacitors share the same current?
It just happens to work out that way. 

Since there's no current through the 5 kohm resistor, you know the voltage \$v_2\$ is equal to the voltage across the 4 kohm resistor, which is of course \$(4\ {\rm k\Omega})i\$.

Also since there's no current through the 5 kohm resistor, you know the current through the 2 kohm resistor is the same as \$i\$, and \$v_1\$ is the same as the voltage across it, so that's \$(2\ {\rm k\Omega})i\$.