Index of embedded networks in the sphere
type: Item
instance of: scholarly article
title: Index of embedded networks in the sphere
author: Gaoming Wang
published in: Journal of Functional Analysis
publication date: 2024-08-01T00:00:00Z
review text: This paper considers networks, namely one-dimensional singular versions of surfaces. As the main result, the Morse index and nullity of stationary triple junction networks in the sphere \(\mathbb{S}^2\) are computed (Theorem 1.1 and in a more formal version Theorem 5.1). The key theorem in the computation is that the index (and nullity) for the whole network is related to the index (and nullity) of smaller networks and the Dirichlet-to-Neumann map defined in the paper (Theorem 1.2). \N\NThe paper is organized into five sections as follows: \N\begin{itemize}\N\item Introduction;\N\item Preliminaries (curves and networks in \(\mathbb{S}^2\), some useful function spaces, examples of eigenfunctions);\N\item The spectrum on networks and the Dirichlet-to-Neumann map (eigenvalues on networks);\N\item Index theorem for networks (Dirichlet-to-Neumann map with respect to a partition);\N\item Index and nullity of the stationary triple junction networks on spheres. \N\end{itemize} A useful appendix ``Computation of Dirichlet-to-Neumann maps'' is given at the end of the paper. Another paper of the author directly connected to this topic is [Calc. Var. Partial Differ. Equ. 61, No. 4, Paper No. 138, 26 p. (2022; Zbl 1502.53014)].
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 7890700
zbMATH Keywords: geodesic networks
zbMATH Keywords: Morse index
zbMATH Keywords: Dirichlet-to-Neumann map
MaRDI profile type: Publication
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DOI: 10.1016/J.JFA.2024.110525
description: scientific article; zbMATH DE number 7890700