Papers › Minimal Lipschitz and ∞-Harmonic Extensions of Vector-Valued Functions on Finite Graphs
Minimal Lipschitz and ∞-Harmonic Extensions of Vector-Valued Functions on Finite Graphs
Miroslav Bačák, Johannes Hertrich, Sebastian Neumayer, Gabriele Steidl
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This paper deals with extensions of vector-valued functions on finite graphs fulfilling distinguished minimality properties. We show that so-called lex and L-lex minimal extensions are actually the same and call them minimal Lipschitz extensions. Then we prove that the solution of the graph p-Laplacians converge to these extensions as p→∞. Furthermore, we examine the relation between minimal Lipschitz extensions and iterated weighted midrange filters and address their connection to ∞-Laplacians for scalar-valued functions. A convergence proof for an iterative algorithm proposed by Elmoataz et al.~(2014) for finding the zero of the ∞-Laplacian is given. Finally, we present applications in image inpainting.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections