图形曲率商方程的内曲率估计
Interior curvature estimates for graphical curvature quotient equations
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中文总结 AI 辅助
本文在完整Gårding锥上证明了曲率商方程可容许图形解的内曲率估计，无需凸性假设，通过压缩不等式、双曲面比较和Pogorelov估计实现。
中文摘要 AI 辅助
我们在完整的Gårding锥$\Gamma_k$上，对范围$3\leq k<n$内的曲率商方程的可容许图形解证明了内曲率估计。不需要凸性、半凸性或$\Gamma_{k+1}$-可容许性假设。证明结合了新的定量压缩不等式、双曲面比较与加倍论证，以及Pogorelov估计。
英文摘要
We prove interior curvature estimates for admissible graphical solutions of curvature quotient equations in the range $3\leq k<n$ on the full Gårding cone $Γ_k$. No convexity, semiconvexity, or $Γ_{k+1}$-admissibility assumption is required. The proof combines a new quantitative compression inequality, a two-surface comparison and doubling argument, and a Pogorelov estimate.
