论文标题
完全非线性方程的均匀熵和能量边界
Uniform entropy and energy bounds for fully non-linear equations
论文作者
论文摘要
背景度量中均匀的能量边界是从上限获得的，用于熵样数量。该论点基于涉及级别集合的辅助蒙格 - 安培等方程，并绕过Alexandrov-Bakelman-Pucci最大原理。特别是，它暗示了系统的统一$ l^\ infty $界限，将完全非线性方程耦合到其线性化，从而推广CSCK方程。
Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Ampère equations involving sublevel sets, and bypasses the Alexandrov-Bakelman-Pucci maximum principle. In particular, it implies uniform $L^\infty$ bounds for systems coupling a fully non-linear equation to its linearization, generalizing the cscK equation.
