  In the present paper, we prove the a priori estimates of Sobolev norms for a
free boundary problem of the incompressible inviscid MHD equations in all
physical spatial dimensions $n=2$ and 3 by adopting a geometrical point of view
used in Christodoulou-Lindblad CPAM 2000, and estimating quantities such as the
second fundamental form and the velocity of the free surface. We identify the
well-posedness condition that the outer normal derivative of the total pressure
including the fluid and magnetic pressures is negative on the free boundary,
which is similar to the physical condition (Taylor sign condition) for the
incompressible Euler equations of fluids.
