论文标题
通过粘度方法来解决曲率问题的恒定等级定理
Constant rank theorems for curvature problems via a viscosity approach
论文作者
论文摘要
几何分析中的一组重要定理由恒定的等级定理组成，用于各种曲率问题。在本文中，对于紧凑型和非压缩设置中的几何曲率问题，我们提供了基本和简短的新证明。此外，我们采用我们的方法来获得新几何设置中均匀和非均匀曲率方程的恒定等级定理。我们方法的重要成分之一是在粘度意义上概括了差异不等式，这是由线性图的最小特征值（Brendle-choi-daskalopoulos，actaMath。219（2017）（2017）：1-16）对一个子跟踪。粘度方法为围绕众所周知的技术障碍提供了一种简洁的方式，而特征值通常只是Lipschitz。这为简单的归纳论点铺平了道路。
An important set of theorems in geometric analysis consists of constant rank theorems for a wide variety of curvature problems. In this paper, for geometric curvature problems in compact and non-compact settings, we provide new proofs which are both elementary and short. Moreover, we employ our method to obtain constant rank theorems for homogeneous and non-homogeneous curvature equations in new geometric settings. One of the essential ingredients for our method is a generalization of a differential inequality in a viscosity sense satisfied by the smallest eigenvalue of a linear map (Brendle-Choi-Daskalopoulos, Acta Math. 219(2017): 1-16) to the one for the subtrace. The viscosity approach provides a concise way to work around the well known technical hurdle that eigenvalues are only Lipschitz in general. This paves the way for a simple induction argument.
