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A Bernstein Theorem for the Self-Shrinking $J$-Equation and Some Generalizations
We prove that every entire smooth strictly plurisubharmonic solution of the self-shrinking $J$-equation on $\mathbb{C}^n$ is a quadratic polynomial. This removes the asymptotic lower bound assumption on the complex Hessian in \cite[Theorem 4]{HJ}. The result also recovers the corresponding real rigi
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