关于Hessian商方程的一个凹性不等式
A Concavity Inequality for Hessian Quotient Equations
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中文总结 AI 辅助
本文利用对称多项式基变换证明Hessian商算子σ_k/σ_{k-1}的凹性不等式，消除了相关方程凸解C²估计的额外假设，还得到初等对称多项式的若干有用不等式。
中文摘要 AI 辅助
我们利用对称多项式的基变换，证明了Hessian商算子σ_k/σ_{k-1}的一个凹性不等式，这消除了此前在σ_k/σ_{k-1}方程凸解的内部C²估计中所施加的额外结构凹性假设，该方法还得到了初等对称多项式的若干有用不等式。
英文摘要
We prove a concavity inequality for the Hessian quotient operator $σ_k/σ_{k-1}$ using a change of basis for symmetric polynomials. This removes an additional structural concavity assumption previously imposed in the interior $C^2$ estimate for convex solutions of the $σ_k/σ_{k-1}$ equation. The method also yields several useful inequalities for elementary symmetric polynomials.
