Hi Gunter, over here I'm able to put on a 0.1mm fillet on that outer border only ok.

But in order to do it, you have to select the outer set of _edges_ - in your model you also have a separate generator curve object sitting right in the same area as the edges. If you select that curve object instead of the edges, then you will not get any fillet result.

Since that curve is overlapping right over the edges it will make it difficult to select the edges - first hide or delete that generator curve object so you can select edges.

You also may want to set up the shortcut for "Select loop" which will help to make an edge selection like this:
http://moi3d.com/forum/index.php?webtag=MOI&msg=3335.5

So first hide the curve that's in the way, then select 2 edges along that upper leaf boundary, then use "Select loop" to get the whole set of edges selected (46 edges there), then run Fillet with a radius of 0.1 and it should work for you. Also you can go more than that, like up to 0.5 or so it looks like.

- Michael