We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2013.04.007}, url = {http://www.sciencedirect.com/science/article/pii/S0294144913000711}, author = {Sara Daneri and Aldo Pratelli} } @article {2013, title = {On Sudakov{\textquoteright}s type decomposition of transference plans with norm costs}, number = {SISSA;51/2013/MATE}, year = {2013}, institution = {SISSA}, url = {http://hdl.handle.net/1963/7206}, author = {Stefano Bianchini and Sara Daneri} } @mastersthesis {2011, title = {Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms}, year = {2011}, school = {SISSA}, abstract = {This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane.}, url = {http://hdl.handle.net/1963/5348}, author = {Sara Daneri} } @article {1110.6124, title = {A planar bi-Lipschitz extension Theorem}, year = {2011}, url = {http://arxiv.org/abs/1110.6124}, author = {Sara Daneri and Aldo Pratelli} } @article {2010, title = {The disintegration of the Lebesgue measure on the faces of a convex function}, journal = {J. Funct. Anal. 258 (2010) 3604-3661}, number = {SISSA;24/2009/M}, year = {2010}, abstract = {We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-\> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

}, doi = {10.1016/j.jfa.2010.01.024}, url = {http://hdl.handle.net/1963/3622}, author = {Laura Caravenna and Sara Daneri} } @article {2008, title = {Eulerian calculus for the displacement convexity in the Wasserstein distance}, journal = {SIAM J. Math. Anal. 40 (2008) 1104-1122}, number = {arXiv.org;0801.2455v1}, year = {2008}, publisher = {SIAM}, abstract = {In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.}, doi = {10.1137/08071346X}, url = {http://hdl.handle.net/1963/3413}, author = {Sara Daneri and Giuseppe Savar{\`e}} }