An energy gap phenomenon for the Whitney sphere

25 Apr 2020  ·  Zhang Liuyang ·

For an immersed Lagrangian submanifold, let $\check{A}$ be the Lagrangian trace-free second fundamental form. In this note we consider the equation $\nabla^*T=0$ on Lagrangian surfaces immersed in $\mathbb{C}^2$, where $T=-2\nabla^*(\check{A}\lrcorner\omega)$, and we prove a gap theorem for the Whitney sphere as a solution to this equation...

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Differential Geometry Analysis of PDEs