  Low-mass M stars are plentiful in the Universe and often host small, rocky
planets detectable with the current instrumentation. Recently, seven small
planets have been discovered orbiting the ultracool dwarf
TRAPPIST-1\cite{Gillon16,Gillon17}. We examine the role of electromagnetic
induction heating of these planets, caused by the star's rotation and the
planet's orbital motion. If the stellar rotation and magnetic dipole axes are
inclined with respect to each other, induction heating can melt the upper
mantle and enormously increase volcanic activity, sometimes producing a magma
ocean below the planetary surface. We show that induction heating leads the
three innermost planets, one of which is in the habitable zone, to either
evolve towards a molten mantle planet, or to experience increased outgassing
and volcanic activity, while the four outermost planets remain mostly
unaffected.
