Here's my problem: on my website, you can click on all the regions, and the new web page is the result of the search of the region. Thus the result may be empty.
Shall I include all those "empty search result" pages in the
sitemap.xml or not?
Yes, submit those pages. They may be empty right now, but they may not be empty when Google crawls them or when a user clicks on the link in the search results. Since the point of the XML Sitemap is to let Google know the page is there, not what the content is, then you should be including those pages.