Is there a good way to maintain your own list of publications on your home page? If you are lazy, you may simply add a link to your list of articles on arXiv.org and to your Google Scholar profile. An elegant alternative solution is to embed automatically your arXiv list of articles using the myarticles widget. This requires to setup an arXiv author-id and to claim or request ownership for articles uploaded by co-authors. You may also add Journal references and digital objects identifiers (DOI) on arXiv to your published articles.
French institutions members may use Hyper Articles en Ligne (HAL) to upload their articles. HAL is able to automatically upload on arXiv, and has the advantage to allow additionally bibliographic entries without documents (arXiv does not). HAL provides moreover automatic publication lists.
You may also cook up a link to a list of publications based on your MR author-id or zbMATH author-id, but the access to these databases is limited by subscription.
You may find an implementation of all that in the source code of my home page.