Some Geometric Calculations on Wasserstein Space
By J. Lott. 2006
193 citations recorded by the source corpus.
We compute the Riemannian connection and curvature for the Wasserstein space of a smooth compact Riemannian manifold.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6666e7bffef8b96421330c721dd9d5907a42841e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Nicola Gigli
- Luigi Ambrosio
- Karl‐Theodor Sturm
- Wilfrid Gangbo
- Andrea Mondino
- Fabio Cavalletti
- Giuseppe Savar'e
- Filippo Santambrogio
In Astronomy and Astrophysics
- Luigi Ambrosio
- Nicola Gigli
- Karl‐Theodor Sturm
- Andrea Mondino
- Wilfrid Gangbo
- Hwa Kil Kim
- T. Pacini
- Adrian Tudorascu
In Geometry and Topology
- Nicola Gigli
- Luigi Ambrosio
- Wilfrid Gangbo
- Benoît R. Kloeckner
- Hwa Kil Kim
- Karl‐Theodor Sturm
- T. Pacini
- Adrian Tudorascu
Citations in the corpus
- The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces (2012, background): “,m)(f) = (X,d+f,m). These results are very much in the spirit of Otto’s Riemannian calculus [Ott01] on the L2-Wasserstein space P2(Rn) which also leads to lower bounds on the sectional curvature (cf. [Lot08]) and quite detailed structural assertions on the tangent space (cf. [AGS05]). The latter, ho”
- Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems (2008, background): “Lott for preliminary versions of their work [24], [28], A.”
- A User’s Guide to Optimal Transport (2013, background): “Lott [56]: rigorous formulas are derived for the computation of such objects on the ‘submanifold’ PC∞(M)”
- On differentiability in the Wasserstein space and well-posedness for Hamilton–Jacobi equations (2019, background): “The metric and the natural Levi-Civita connection on H are linked to the metric and the Levi-Civita connection [17] [18] on P2(R) (cf.”
- Understanding MCMC Dynamics as Flows on the Wasserstein Space (2019, background): “Lott (2008) considers the Poisson structure Eq.”
- A geometric study of Wasserstein spaces: Euclidean spaces (2008, methodology): “In particular the L2 Wasserstein space W2(X) have been used by Von Renesse and Sturm [15], Sturm [17] and Lott and Villani [12] to define certain curvature conditions on a metric space X .”
- CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES (2019, background): “Lott and C. Villani’s one Lott and Villani [2009] uses a more general classes of entropies, not necessarily power-like, singled out by R.”