Formal Riemannian Structure of the Wasserstein metric

The Wasserstein metric is defined as

W_{2}(\mu ,\nu ):=\min _{\gamma \in \Gamma (\mu ,\nu )}\left(\int |x_{1}-x_{2}|^{2}\,d\gamma (x_{1},x_{2})\right)^{1/2}

Basic Structure of Riemannian Manifolds

Tangent Space Induced by Wasserstein Metric

Riemannian Metric Induced by Wasserstein Metric

References

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Formal Riemannian Structure of the Wasserstein metric

Contents

Basic Structure of Riemannian Manifolds

Tangent Space Induced by Wasserstein Metric

Riemannian Metric Induced by Wasserstein Metric

References

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Formal Riemannian Structure of the Wasserstein metric

Basic Structure of Riemannian Manifolds

Tangent Space Induced by Wasserstein Metric

Riemannian Metric Induced by Wasserstein Metric

References

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