AI 中文总结
本文针对椭圆型Weingarten曲率商方程的严格凸解，借助方程算子的凹性不等式与新颖辅助函数，通过初等最大值原理证明其先验内部曲率界，还得到低维特殊拉格朗日曲率方程严格凸解的对应估计。
AI 中文摘要
在本注记中，我们证明了椭圆型Weingarten曲率商方程严格凸解的先验内部曲率界。该证明未采用涉及积分估计或紧性论证的高级方法，而是依赖于方程算子的一个凹性不等式及辅助函数的新颖选取，以开展初等最大值原理论证。作为推论，低维下特殊拉格朗日曲率方程严格凸解的内部曲率估计也成立。
英文摘要
In this note, we prove a priori interior curvature bounds for strictly convex solutions to elliptic Weingarten curvature quotient equations. The proof does not employ the advanced methods involving integral estimates or compactness arguments. Instead, it relies on a concavity inequality for the equation operator and a novel choice of the auxiliary function to carry out an elementary maximum-principle argument. Interior curvature estimates for strictly convex solutions to the special Lagrangian curvature equation in low dimensions also follow as a consequence.
Commentsv2: fixed typos throughout the manuscript
