Spectral minimal partitions for a thin strip on a cylinder or a thin annulus like domain with Neumann condition

嵌入环形区域在耦合曲线缩短流和二维里奇流下的定量谱稳定性

Quantitative Spectral Stability for an Embedded Annulus under Coupled Curve Shortening and $2$D Ricci Flows

该研究通过变分公式和调和容量方法，分析了嵌入环形区域在耦合曲线缩短流和二维里奇流下的谱稳定性，并建立了谱隙估计与几何亏损的关系。

Minimal partitions for anisotropic tori

We analyze spectral minimal $k$-partitions for the torus. In continuation with what we have obtained for thin annuli or thin strips on a cylinder (Neumann case), we get similar results for anisotropic tori.

Waveguides with combined Dirichlet and Robin boundary conditions

We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infi…

计算最低朗道能级以下的特征值数量

Counting eigenvalues below the lowest Landau level

本文研究有界平面区域上磁拉普拉斯算子在混合边界条件下低于最低朗道能级的特征值数量，通过分离变量和纤维算子方法对带状区域与圆环区域进行量化比较。

扰动圆柱中的变量分离

Separation of variables in perturbed cylinders

本文研究二维扰动圆柱域上Dirichlet边界条件的Laplace算子特征值问题，通过映射和Fourier分解分离变量，数值求解ODE系统得到特征值及复共振，并应用于量子波导。

关于 $\mathbb{S}^1 \times \R$ 上的 Pólya 猜想

Pólya's conjecture on $\mathbb{S}^1 \times \R$

本文研究无限圆柱体上两类等周区域满足 Pólya 猜想的面积范围，给出测地圆盘半径上界并完整刻画圆柱条带高度条件，进而得到给定面积等周区域满足猜想的充要条件。