论文标题
完整指标的共形类别的部分均匀椭圆性和规定的问题
The partial uniform ellipticity and prescribed problems on the conformal classes of complete metrics
论文作者
论文摘要
我们通过计算线性化运算符的大量特征值来阐明二阶完全非线性方程的近距离椭圆度如何均匀。这提出了一种有效而新颖的方法，可以理解椭圆形和抛物线类型的完全非线性方程的结构。作为应用程序，我们解决了Loewner-Nirenberg问题的完全非线性版本，并解决了完全非线性Yamabe问题的非2CACT完整版本。正如拓扑阻塞所示，我们的方法很精致。
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully nonlinear equations of elliptic and parabolic type. As applications, we solve a fully nonlinear version of the Loewner-Nirenberg problem and a noncompact complete version of fully nonlinear Yamabe problem. Our method is delicate as shown by a topological obstruction.
