  We demonstrate the continuous translational invariance of the energy of a
capillary surface in contact with reconfigurable solid boundaries. We present a
theoretical approach to find the energy-invariant equilibria of spherical
capillary surfaces in contact with solid boundaries of arbitrary shape and
examine the implications of dynamic frictional forces upon a reconfiguration of
the boundaries. Experimentally, we realise our ideas by manipulating the
position of a droplet in a wedge geometry using lubricant-impregnated solid
surfaces, which eliminate the contact-angle hysteresis and provide a test bed
for quantifying dissipative losses out of equilibrium. Our experiments show
that dissipative energy losses for an otherwise energy-invariant
reconfiguration are relatively small, provided that the actuation timescale is
longer than the typical relaxation timescale of the capillary surface. We
discuss the wider applicability of our ideas as a pathway for liquid
manipulation at no potential energy cost in low-pinning, low-friction
situations.
