Year: 2021
Type: preprint
Abstract: We introduce the Steklov flows on finite trees, i.e. the flows (or currents) associated with the Steklov problem. By constructing appropriate Steklov flows, we prove the monotonicity and rigidity of the first nonzero Steklov eigenvalues on trees: for finite trees $\g_1$ and $\g_2,$ the first nonzero Steklov eigenvalue of $\g_1$ is greater than or equal to that of $\g_2$, provided that $\g_1$ is a subgraph of $\g_2.$ Moreover, we give the sufficient and necessary condition in which the equality holds.
Source: arXiv (Cornell University)
Authors: He, Zunwu, Hua, Bobo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3135976213