The current function of getting a "Link to this Report" only provides a URL to that static report for the dates you are viewing - it does not let you distribute a URL for relative time frame (e.g. Yesterday, this month, etc.). Apart from making it more useful when sending links to others, it is the only method of linking to reports that you can not put on a Dashboard (text box reportlet with URL) but of course these do not work if Static.
IDEA: Please make the URL's for reports for relative time periods just like when adding to Dashboards (i.e. Fixed & Rolling dates)