# Non-existence of optimal transport maps for the multi-marginal repulsive harmonic cost

arXiv: https://arxiv.org/abs/1805.00417 · HTML: https://mlsanity.com/paper/1805.00417/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2018.

## Built on by (most cited first, 1 of 1)

- [The GenCol algorithm for high-dimensional optimal transport: general formulation and application to barycenters and Wasserstein splines](https://mlsanity.com/paper/2209.09081/) (2022)

## Abstract (arXiv)

We give an example of an absolutely continuous measure μ on mathbb Rd, for any d ≥ 1, such that no minimizer of the 3-marginal harmonic repulsive cost with all marginals equal to μ is supported on a graph over the first variable.