Sharp Geometric Upper Bounds on Resonances for Surfaces with Hyperbolic Ends
Sharp Geometric Upper Bounds on Resonances for Surfaces with Hyperbolic Ends
复制标题
双曲端面共振的尖锐几何上限
DOI：
10.2140/apde.2012.5.513
复制
发表时间：
2010
期刊：
影响因子：
2.2
通讯作者：
D. Borthwick
中科院分区：
文献类型：
--
作者：
D. Borthwick
我们建立了一个尖锐的几何常数上界的共振计数函数的曲面双曲结束。在某些致密核内允许任意度量，并且端部可以是双曲平面、漏斗或尖点类型。上限中的常数仅取决于芯的体积和与漏斗或双曲线平面端部相关联的长度参数。我们的估计是尖锐的，因为它再现了精确的渐近常数的情况下，有限面积曲面的双曲尖端，以及在漏斗端的Dirichlet边界condtiions。
We establish a sharp geometric constant for the upper bound on the resonance counting function for surfaces with hyperbolic ends. An arbitrary metric is allowed within some compact core, and the ends may be of hyperbolic planar, funnel, or cusp type. The constant in the upper bound depends only on the volume of the core and the length parameters associated to the funnel or hyperbolic planar ends. Our estimate is sharp in that it reproduces the exact asymptotic constant in the case of finite-area surfaces with hyperbolic cusp ends, and also in the case of funnel ends with Dirichlet boundary condtiions.