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<p>We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Ampère equation, the quaternionic Hessian equation and the Monge-Ampère equation for quaternionic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((n-1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperkähler manifolds satisfy a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C^{2,\alpha }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>α</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> a priori estimate.</p>

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Fully non-linear elliptic equations on compact hyperkähler manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月17日

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  • Giovanni Gentili,
  • Luigi Vezzoni

摘要

We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Ampère equation, the quaternionic Hessian equation and the Monge-Ampère equation for quaternionic \((n-1)\) ( n - 1 ) -plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperkähler manifolds satisfy a \(C^{2,\alpha }\) C 2 , α a priori estimate.