  We studied the curvature-driven roughening of a disk domain pattern with a
variable interface window. The relaxation of interface is driven by negative
surface tension . When a domain boundary propagates radially at a constant
rate, we found that evolution of interface roughness follows scaling dynamic
behavior. The local growth exponents are substantially different from the
global exponents. Curvature-driven roughening belongs to a new class of
anomalous roughening dynamics. However, a different surface tension leads to
different global exponents. This is different from that of interface evolution
with a fixed-size window, which has universal exponent. The variable growth
window leads to a new class of anomalous roughening dynamics.
