Example 4.2 . [04D3]
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Example 4.2.
Schoen and Wolfson [67] found area minimizers within certain Lagrangian isotopy classes, which are not minimal surfaces.4646 46 There is no contradiction: area minimisation among Lagrangians by no means guarantee area stationarity among submanifold. The Brakke flow with such initial data further decreases mass in time, so must cease to be Lagrangian. However, these examples are not graded, so do not contradict Joyce’s program. A possible lesson is that non-graded Lagrangians are bad.