二维拟共形映射与周期谱问题
Quasi-conformal mappings and periodic spectral problems in dimension two
摘要：
研究了二维二阶周期系数椭圆算子的谱性质。这些运营商的作用在周期性的简单连接波导，无论是狄利克雷，或诺依曼，或第三边界条件。主要的结果是绝对连续的谱，这样的运营商。证明的基石是变量的等温变量变换，将度量减小到平坦的度量，将波导减小到直条。主要的技术工具是黎曼映射定理的准共形变体。
英文摘要：
We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition. The main result is the absolute continuity of the spectra of such operators. The corner stone of the proof is an isothermal change of variables, reducing the metric to a flat one and the waveguide to a straight strip. The main technical tool is the quasi-conformal variant of the Riemann mapping theorem.
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