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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…
Probabilistic intersection theory in Riemannian homogeneous spaces
Paul Breiding, Peter Bürgisser, Antonio Lerario +1
Let be a Riemannian homogeneous space, where is a compact Lie group with closed subgroup . Classical intersection theory states that the de Rham cohomology ring of $…
The Grassmann distance complexity
Antonio Lerario, Andrea Rosana
Motivated by the concept of Euclidean Distance Degree, which measures the complexity of finding the nearest point to an algebraic set in Euclidean space, we introduce the notion of…
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…