  Solid sheets and fluid membranes exhibit buckling under lateral compression.
Here, it is revealed that fluid membranes have anisotropic buckling surface
tension contrary to solid sheets. Surprisingly, the surface tension
perpendicular to the buckling direction shows stronger dependence than that
parallel to it. Our theoretical predictions are supported by numerical
simulations of a meshless membrane model. This anisotropic tension can be used
to measure the membrane bending rigidity. It is also found phase
synchronization occurs between multilayered buckled membranes.
