Can the object created by Minor Illusion be carried or worn?

Looking at the RAW for Minor Illusion (PHB, page 260) and other questions, I recognize that Minor Illusion is very limited in its ability to move on its own or change its appearance. However, I’m wondering if the illusory object can be carried or worn as demonstrated in two examples:

  1. I want to convince a visiting noble that I’m the ruler of this small town, so before I meet him in the city center, I cast Minor Illusion to create a crown on my head. Assuming he doesn’t investigate (or fails) does it continue to sit naturally upon my head through normal movements?

  2. I’ve just stolen a historical battleaxe and the guard have been alerted to its absence. Can I choose someone who is rapidly walking away and cast an illusory version of the battleaxe strapped to his back as a diversion? Does this usage work until the illusion is investigated or interacted with (as normal.)