问题:

How does a Silverlight application ask the browser what domain its being served up from?

UPDATE: Make sure if your class doesn't already have this using statement add it at the top your class. This will help you on some of the examples you'll see online. It confused me for a bit.

  using System.Windows.Browser;

回答1:

How about HtmlDocument.DocumentUri? That'd get you what you need. Page about browser interop here.

回答2:

As jcollum says you access the HtmlDocument.DocumentUri property to get lots of information on the host. To answer the question in your comment this is how you do this in Page.xaml.cs:

using System;
using System.Windows.Browser;
using System.Windows.Controls;

namespace SilverlightApplication1
{
    public partial class Page : UserControl
    {
        public Page()
        {
            InitializeComponent();

            string hostName = HtmlPage.Document.DocumentUri.Host;
            int port = HtmlPage.Document.DocumentUri.Port;
        }
    }
}