Abstract We study self-expanding solutions $M^{m}\subset \mathbb {R}^{n}$ M m ⊂ ℝ n of the mean curvature flow. One our main results is, that complete convex hypersurfaces are products curves and ...

The goal of this paper is to introduce the approximated convex envelope of a function and to estimate how it differs from its convex envelope. Such a problem arises in various physical situations where the function considered is some energy that has to be minimized.This study is a first step toward understanding how to approximate the quasi-convex envelope of a function. The importance of this ...

We consider the space, CR(M), consisting of CR functions which also lie in L(M) on a quadric submanifold M of C of codimension at least one. For 1 ≤ p ≤ ∞, we prove that each element in CR(M) extends uniquely to an H function on the interior of the convex hull of M . As part of the proof, we establish a semi-global version of the CR approximation theorem of Baouendi and Treves for submanifolds ...

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Truncated convex models (TCM) are a special case of pairwise random fields that have been widely used in computer vision. However, by restricting the order of the potentials to be at most two, they fail to capture useful image statistics. We propose a natural generalization of TCM to high-order random fields, which we call truncated max-of-convex models (TMCM). The energy function of TMCM consi...

The coordination sequence of a lattice L encodes the word-length function with respect toM , a set that generates L as a monoid. We investigate the coordination sequence of the cyclotomic lattice L = Z[ζm], where ζm is a primitive m th root of unity and where M is the set of all m roots of unity. We prove several conjectures by Parker regarding the structure of the rational generating function ...

Lin and Chang gave a generating function of convex polyominoes with an m+1 by n + 1 minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is m+ n+mn m+ n ( 2m+ 2n 2m ) − 2mn m+ n ( m+ n m )2 . We show that this result can be derived from some binomial coefficients identities related to the generating function of Jacobi polynomials. Some (binomia...

Aproximity theorem is astatement that, given an optimization problem and its relaxation, an optimal solution to the original problem exists in acertain neighborhood of asolution to the relaxation. Proximity theorems have been used successfully, for example, in designing efficient algorithms for discrete resource allocation problems. After reviewing the recent results for $\mathrm{L}$-convex and...