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The constant rank theorem was initially developed by Caffarelli-Friedman in 1985 in two-dimensions for convex solutions of semilinear equations. Later, Korevaar-Lewis extended the result to higher dim...
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data anal- ysis, has been successfully used in several applications, such as in collaborative filtering to design reco...
In this paper we are interested in functions defined, on a set of matrices, by the mean of quadratic forms and we compute the rank-one-convex, quasiconvex, polyconvex and convex envelopes of these fun...
We report on an attempt to find a counterexample to the statement that rank-one convexity does not imply quasiconvexity in the case of 2$\times$2 matrices. The failure of such attempt is a consequence...
We define $p$-rank-one connections at infinity for an unbounded set $K$ in $M^{N\times n}$ and show that the quasiconvex hull $Q_p(K)$ may be bigger than $K$ if $K$ has a $p$-rank-one connection, wher...

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