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Free maps in critical dimension on
Roberto De Leo
The critical dimension for free maps on m-manifolds is . We show that for every . The main tool is a…
Partially Isometric Immersions and Free Maps
Giuseppina D'Ambra, Roberto De Leo, Andrea Loi
In this paper we investigate the existence of ``partially'' isometric immersions. These are maps f:M->R^q which, for a given Riemannian manifold M, are isometries on some sub-bundl…
Solvability of the cohomological equation for regular vector fields on the plane
Roberto De Leo
We consider planar vector field without zeroes X and study the image of the associated Lie derivative operator LX acting on the space of smooth functions. We show that the cokernel…
Topology of plane sections of periodic polyhedra with an application to the Truncated Octahedron
Roberto De Leo
The main results of A. Zorich and I. Dynnikov about plane sections of periodic surfaces are extended to the PL case. As an application, the Stereographic Map of a truncated octahed…