Brouwer degree for Kazdan-Warner equations on a connected finite graph
Differential Geometry
2021-04-21 v1 Analysis of PDEs
Combinatorics
Functional Analysis
Abstract
We study Kazdan-Warner equations on a connected finite graph via the method of the degree theory. Firstly, we prove that all solutions to the Kazdan-Warner equation with nonzero prescribed function are uniformly bounded and the Brouwer degree is well defined. Secondly, we compute the Brouwer degree case by case. As consequences, we give new proofs of some known existence results for the Kazdan-Warner equation on a connected finite graph.
Keywords
Cite
@article{arxiv.2104.09881,
title = {Brouwer degree for Kazdan-Warner equations on a connected finite graph},
author = {Linlin Sun and Liuquan Wang},
journal= {arXiv preprint arXiv:2104.09881},
year = {2021}
}
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23 pages