论文标题
组合图上的最小steklov特征值
Minimal Steklov eigenvalues on combinatorial graphs
论文作者
论文摘要
在本文中，我们通过扩展Friedman的理论[Duke Math。 J. 69（1993），否。 3，487--525]用于laplacian本征的结构域，用于steklov eigenfunctions，并在组合图上解决了steklov eigenvalues的极端问题，这是Friedman解决的极端问题的类似物，这是Friedman [Duke Math [Duke Duke Math]解决的极端问题。 J. 83（1996），否。 1，1--18。]对于拉普拉斯的特征值。更确切地说，我们主要表明，$ i^{\ rm th} $ steklov eigenvalue在连接的组合图上与$ n $ dertices在连接的组合图上实质上是由一颗恒星与每只手臂一起使用$ i \ not | n $的，并在每种牙齿的牙齿上，并在$ i n $上固定时，并在$ i | n $上进行$ i $ i $ i | n $ i | n时。
In this paper, we study extremal problems of Steklov eigenvalues on combinatorial graphs by extending Friedman's theory [Duke Math. J. 69 (1993), no. 3, 487--525] of nodal domains for Laplacian eigenfunctions to Steklov eigenfunctions, and solve an extremal problem for Steklov eigenvalues on combinatorial graphs that is an analogue of the extremal problem solved by Friedman [Duke Math. J. 83 (1996), no. 1, 1--18.] for Laplacian eigenvalues. More precisely, we mainly show that the minimum of the $i^{\rm th}$ Steklov eigenvalue on a connected combinatorial graph with $n$ vertices is essentially attained by a star with each arm a minimal broom when $i\not|n$, and attained by a regular comb with each tooth a minimal broom when $i|n$.
