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<p>In this paper, we establish the <i>a priori</i> estimates for solutions of mixed Hessian quotient type equations on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{S}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msup> </math></EquationSource> </InlineEquation>. Then we obtain the existence and uniqueness of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\tilde{\Gamma}_{k}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mover> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">~</mo> </mover> </mrow> <mrow> <mi>k</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>-admissible solutions to the <i>L</i><sub><i>p</i></sub> dual Minkowski type problem with <i>p</i> ≥ <i>q</i>. Moreover, we show the existence of convex solutions by Constant Rank Theorem.</p>

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The Lp dual Minkowski type problem for mixed Hessian quotient type equations with p ≥ q

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Ni Xiang,
  • Yuni Xiong

摘要

In this paper, we establish the a priori estimates for solutions of mixed Hessian quotient type equations on \(\mathbb{S}^{n}\) S n . Then we obtain the existence and uniqueness of \(\tilde{\Gamma}_{k}\) Γ ~ k -admissible solutions to the Lp dual Minkowski type problem with p ≥ q. Moreover, we show the existence of convex solutions by Constant Rank Theorem.