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9 papers · 1 filter
Log-Euclidean Lie Groups
Olivier Bisson, Xavier Pennec
We develop a self-contained theory of log-Euclidean Lie groups: smooth manifolds diffeomorphic to finite-dimensional vector spaces, equipped with the pullback of a constant Euclide…
Barycentric subspace analysis of network-valued data
Elodie Maignant, Xavier Pennec, Alain Trouvé +1
Certain data are naturally modeled by networks or weighted graphs, be they biological networks or mobility networks. When there is no canonical labeling of the nodes across the dat…
Not all sub-Riemannian minimizing geodesics are smooth
Yacine Chitour, Frédéric Jean, Roberto Monti +4
A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an exa…
Maximality of the futures of points in globally hyperbolic maximal conformally flat spacetimes
Rym Smaï
Let M be a globally hyperbolic conformally spacetime. We prove that the indecomposable past/future sets (abbrev. IPs/IFs) -in the sense of Penrose, Kronheimer and Geroch -of the un…
Positivity, cross-ratios and the Collar Lemma
Jonas Beyrer, Olivier Guichard, François Labourie +2
We prove that -positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are pos…
Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions
A Belotto da Silva, A Parusiński, L Rifford
Given a smooth totally nonholonomic distribution on a smooth manifold, we construct a singular distribution capturing essential abnormal lifts which is locally generated by vector…