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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.

7 votes
2 answers
178 views

Graph embedding that locally minimizes total edge lengths

I consider a graph $G$ (possibly infinite, but locally finite) embedded in the Euclidean plane $\mathbb{E}^2 \cup \{\infty\}$ such that each local perturbation of the embedding "increases the total le …
Hao Chen's user avatar
  • 2,581
1 vote

Graph embedding that locally minimizes total edge lengths

Finally, I find that the works of Ivanov and Tuzhilin seem to be very close to what I'm looking for.
Hao Chen's user avatar
  • 2,581