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.

VL - 31 UR - http://www.sciencedirect.com/science/article/pii/S0294144913000711 ER - TY - RPRT T1 - On Sudakov's type decomposition of transference plans with norm costs Y1 - 2013 A1 - Stefano Bianchini A1 - Sara Daneri PB - SISSA UR - http://hdl.handle.net/1963/7206 U1 - 7234 U2 - Mathematics U4 - -1 ER - TY - THES T1 - Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms Y1 - 2011 A1 - Sara Daneri AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/5348 U1 - 5178 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - A planar bi-Lipschitz extension Theorem Y1 - 2011 A1 - Sara Daneri A1 - Aldo Pratelli UR - http://arxiv.org/abs/1110.6124 ER - TY - JOUR T1 - The disintegration of the Lebesgue measure on the faces of a convex function JF - J. Funct. Anal. 258 (2010) 3604-3661 Y1 - 2010 A1 - Laura Caravenna A1 - Sara Daneri AB -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.

UR - http://hdl.handle.net/1963/3622 U1 - 682 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Eulerian calculus for the displacement convexity in the Wasserstein distance JF - SIAM J. Math. Anal. 40 (2008) 1104-1122 Y1 - 2008 A1 - Sara Daneri A1 - Giuseppe Savarè AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/3413 U1 - 922 U2 - Mathematics U3 - Functional Analysis and Applications ER -