Min-max embedded geodesic lines in asymptotically conical surfaces
Min-max embedded geodesic lines in asymptotically conical surfaces
复制标题
渐近圆锥曲面中的最小-最大嵌入测地线
DOI：
10.4310/jdg/1563242470
复制
发表时间：
2016
影响因子：
2.5
通讯作者：
Camillo De Lellis
中科院分区：
文献类型：
--
作者：
A. Carlotto;Camillo De Lellis
我们采用最小-最大的方法来构建不可数的许多，几何上不同的，适当嵌入的测地线在任何渐近锥形表面的非负标量曲率，设置最小化方案注定要失败。我们的建设提供了控制的莫尔斯指数的测地线，我们生产，这将始终小于或等于1（与平等适当的曲率或genericity假设），以及他们的精确渐近行为。事实上，我们可以证明，在任何这样的曲面中，对于每对相对的半直线，都存在一条嵌入测地线，其两端在适当的意义下渐近于这些半直线。
We employ min-max methods to construct uncountably many, geometrically distinct, properly embedded geodesic lines in any asymptotically conical surface of non-negative scalar curvature, a setting where minimization schemes are doomed to fail. Our construction provides control of the Morse index of the geodesic lines we produce, which will be always less or equal than one (with equality under suitable curvature or genericity assumptions), as well as of their precise asymptotic behaviour. In fact, we can prove that in any such surface for every couple of opposite half-lines there exists an embedded geodesic line whose two ends are asymptotic, in a suitable sense, to those half-lines.