arXiv
Open Access
2020
Differentiable maps between Wasserstein spaces
Bernadette Lessel
Thomas Schick
Abstrak
A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a global definition of differentiability, i.e. without a prior notion of pointwise differentiability. With our definition, however, we recover the expected properties of a differential. Special focus is being put on differentiability properties of pushforward maps induced by smooth maps between the underlying manifolds, and on convex mixing of differentiable maps, with an explicit construction of the differential.
Topik & Kata Kunci
Penulis (2)
B
Bernadette Lessel
T
Thomas Schick
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2020
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