论文标题
通过潜在的理论来检测鳍歧管的完整性
Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian
论文作者
论文摘要
在本文中，我们研究了Finsler歧管$ M $的Eikonal和Infinity Laplace操作员的一些潜在理论方面。我们的主要结果表明，可以根据liouville属性和无穷大的最大原则检测到$ m $的远期完整性，包括合适的不等式的亚物业，包括$δ^n_ \ infty U \ ge g（u）$。此外，事实证明，$ \ infty $ a的产能标准和Ekeland原理的粘度版本相当于$ m $的远期完整性。一部分证明是在相对紧凑的集合上的$δ^n_ \ infty U = g（u）$的解决方案的新的边界到内部的Lipschitz估计上取决于的，这意味着对于某些整个有限的解决方案而言，均匀的Lipschitz估计不需要$ M $。
In this paper, we study some potential theoretic aspects of the eikonal and infinity Laplace operator on a Finsler manifold $M$. Our main result shows that the forward completeness of $M$ can be detected in terms of Liouville properties and maximum principles at infinity for subsolutions of suitable inequalities, including $Δ^N_\infty u \ge g(u)$. Also, an $\infty$-capacity criterion and a viscosity version of Ekeland principle are proved to be equivalent to the forward completeness of $M$. Part of the proof hinges on a new boundary-to-interior Lipschitz estimate for solutions of $Δ^N_\infty u = g(u)$ on relatively compact sets, that implies a uniform Lipschitz estimate for certain entire, bounded solutions without requiring the completeness of $M$.
