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An energy gap phenomenon for the Whitney sphere

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In this paper, we study Lagrangian surfaces satisfying $$\nabla ^*T=0$$ ∇ ∗ T = 0 , where $$T=-2\nabla ^*(\check{A}\lrcorner \omega )$$ T = - 2 ∇ ∗ ( A ˇ… Click to show full abstract

In this paper, we study Lagrangian surfaces satisfying $$\nabla ^*T=0$$ ∇ ∗ T = 0 , where $$T=-2\nabla ^*(\check{A}\lrcorner \omega )$$ T = - 2 ∇ ∗ ( A ˇ ⌟ ω ) and $$\check{A}$$ A ˇ is the Lagrangian trace-free second fundamental form. We obtain a gap lemma for such a Lagrangian surface.

Keywords: phenomenon whitney; whitney sphere; energy gap; gap phenomenon

Journal Title: Mathematische Zeitschrift
Year Published: 2019

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