论文标题
稳定最小表面的面积和光谱估计值
Area and spectrum estimates for stable minimal surfaces
论文作者
论文摘要
本说明涉及三维歧管中完全稳定最小表面的面积生长和底部光谱，标量曲率从下面界定。当环境歧管是欧几里得空间时，通过基本参数，直接从稳定性不等式中表明，这种最小表面的面积完全像欧几里得平面一样生长。因此，必须在这种最小的表面上，这是由于Fisher-Colbrie和Schoen以及Carmo和Peng的众所周知的结果。在环境歧管是双曲线空间的情况下，也得出了显式区域生长估计。对于底部频谱，根据环境歧管的标态曲率下限建立上限估计值。
This note concerns the area growth and bottom spectrum of complete stable minimal surfaces in a three-dimensional manifold with scalar curvature bounded from below. When the ambient manifold is the Euclidean space, by an elementary argument, it is shown directly from the stability inequality that the area of such minimal surfaces grows exactly as the Euclidean plane. Consequently, such minimal surfaces must be at, a well-known result due to Fisher-Colbrie and Schoen as well as do Carmo and Peng. In the case the ambient manifold is the hyperbolic space, explicit area growth estimate is also derived. For the bottom spectrum, upper bound estimates are established in terms of the scalar curvature lower bound of the ambient manifold.
