Noncommutative Minimal Surface In Moyal Product

In this paper, we will study Moyal product in Nambu bracket, and define the mini-mal surface by the noncommutative harmonic map. Like Lie algebra, we can define the differential operator and curvature of the noncommutative surface. We prove that a non-commutative surface is minimal if and only if its noncommutative mean curvature vanishes.