论文标题
LaGéométriede bakry-émery等人
La géométrie de Bakry-Émery et l'écart fondamental
论文作者
论文摘要
本文简要介绍了围绕基本差距的结果。我们首先回忆巴克里（Bakry）的几何形状，并展示了拉普拉斯（Laplacian）特征值与迪里奇（Dirichlet）和诺伊曼（Neumann）边界条件之间的联系。然后，我们展示了基本差距与巴克里 - 杰克 - 埃默里的几何形状之间的联系，最后介绍了安德鲁斯（Andrews）和克鲁特巴克（Clutterbuck）的基本差距猜想的证明。最后，我们以三角形和简洁的基本差距的结果介绍了结果。
This article is a brief presentation of results surrounding the fundamental gap. We begin by recalling Bakry-Emery geometry and demonstrate connections between eigenvalues of the Laplacian with the Dirichlet and Neumann boundary conditions. We then show a connection between the fundamental gap and Bakry-Emery geometry, concluding with a presentation of the key ideas in Andrews's and Clutterbuck's proof of the fundamental gap conjecture. We conclude with a presentation of results for the fundamental gap of triangles and simplices.
