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A sub-Riemannian endpoint map with no regular values
Antonio Lerario, Luca Rizzi, Daniele Tiberio
We construct an endpoint map with no regular values, disproving the sub-Riemannian Sard conjecture. Remarkably, in our construction the minimizing Sard property remains valid.
Sard property for rank 2 polarizations in metabelian Lie groups
Enrico Le Donne, Antonio Lerario, Luca Nalon +2
We provide sharp bounds on the dimension of the abnormal set for rank polarizations on metabelian Lie groups, establishing the Sard property for the end-point map of such group…
Sard properties for polynomial maps in infinite dimension
Antonio Lerario, Luca Rizzi, Daniele Tiberio
Sard's theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional B…