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Semantic Scholar Open Access 2020 4 sitasi

Differentiable maps between Wasserstein spaces

Bernadette Lessel Thomas Schick Max Planck Institute for the History of Science Berlin Mathematisches Institut Universitat Gottingen
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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

Mathematics

Penulis (4)

B

Bernadette Lessel

T

Thomas Schick Max Planck Institute for the History of Science

B

Berlin Mathematisches Institut

U

Universitat Gottingen

Format Sitasi

APA MLA BibTeX
Lessel, B., Science, T.S.M.P.I.f.t.H.o., Institut, B.M., Gottingen, U. (2020). Differentiable maps between Wasserstein spaces. https://www.semanticscholar.org/paper/c55557b4771cecbec468eea7ed939d81c0a1afc2

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Tahun Terbit
2020
Bahasa
en
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Semantic Scholar
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Open Access ✓