Reminds me of some interesting papers that are related to this topic, off the top of my head check out [0-1]. Perhaps relative geodesics is a key word to search

Reminds me of some interesting papers that are related to this topic, off the top of my head check out [0-1]. Perhaps relative geodesics is a key word to search. If you picture curves as made out of some sort of pliable material, you can ask how much energy does it take to deform one curve into another. [0] https://arxiv.org/pdf/1305.3572.pdf https://arxiv.org/pdf/1305.3572.pdf [1] https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2016.0619 https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2016...