# Areas on the space of smooth probability density functions on S2

arXiv: https://arxiv.org/abs/2110.07773 · HTML: https://mlsanity.com/paper/2110.07773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 20 references that are in the map.
- First posted on arXiv 14 Oct 2021.

## Builds on (most cited first, 1 of 1)

- [Second order models for optimal transport and cubic splines on the Wasserstein space](https://mlsanity.com/paper/1801.04144/) (2018)

## Abstract (arXiv)

We present symbolic and numerical methods for computing Poisson brackets on the spaces of measures with positive densities of the plane, the 2-torus, and the 2-sphere. We apply our methods to compute symplectic areas of finite regions for the case of the 2-sphere, including an explicit example for Gaussian measures with positive densities.