After Starling is created, you can add an Event.RESIZE listener to the native stage:
this._starling = new Starling(RootClass, this.stage);
this.stage.addEventListener(Event.RESIZE, stage_resizeHandler, false, int.MAX_VALUE, true);
In the listener, you can update the dimensions of the Starling stage and view port to match the dimensions of the native stage:
private function stage_resizeHandler(event:Event):void
{
this._starling.stage.stageWidth = this.stage.stageWidth;
this._starling.stage.stageHeight = this.stage.stageHeight;
var viewPort:Rectangle = this._starling.viewPort;
viewPort.width = this.stage.stageWidth;
viewPort.height = this.stage.stageHeight;
try
{
this._starling.viewPort = viewPort;
}
catch(error:Error) {}
}