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<p>We prove that a complete solution for the complex Monge-Ampère equation (1.1) on ℂ<sup><i>n</i></sup> which is bounded from below by <i>n</i> totally real linear functions to the power greater than <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2n\over{n+1}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mfrac> <mrow> <mn>2</mn> <mi>n</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </math></EquationSource> </InlineEquation> must be trivial.</p>

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Gradient estimates and a Liouville theorem of complex Monge-Ampère equations

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Bing-Long Chen

摘要

We prove that a complete solution for the complex Monge-Ampère equation (1.1) on ℂn which is bounded from below by n totally real linear functions to the power greater than \(2n\over{n+1}\) 2 n n + 1 must be trivial.