A simple closed curve dividing a symplectic two-sphere into two regions of equal area cannot be displaced by a symplectic isotopy. Any disjoint image would lie in one complementary disc, yet it would still have to bound a disc of half the total area.

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  1. Lagrangian displacement (symplectic geometry)
  2. Lagrangian submanifold
  3. Symplectic manifold
  4. Symplectic geometry
  5. Differential geometry
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