Here for a smooth bounded Euclidean domain Ω and a smooth Riemannian manifold N , we show that almost every smooth map φ : ∂Ω→ N serves as boundary data for at most one energy minimizing map u : Ω→ N [Theorem 5.2]. We also obtain some uniform boundary regularity estimates for energy minimizers [Theorem 2.1], which not only are important to our proof, but also imply some other properties of ener...

Abstract. Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic polynomial and Stanley’s theorem relating negative evaluations of the chromatic polynomial to acyclic orientatio...

We develop a systematic method to construct the boundary states in the coset conformal field theory G/H . Based on the relation of the G/H theory with the tensor product theory G×H , we give a map from the boundary states of G×H to those of G/H . Our map provides a large class of boundary states in coset theories, which include those not factorizable into the G and the H sectors. The action of ...

The pseudodeterminant pdet(M) of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If ∂ is a symmetric or skewsymmetric matrix then pdet(∂∂t) = pdet(∂)2. Whenever ∂ is the kth boundary map of a self-dual CWcomplex X, this linear-algebraic identity implies that the torsion-weighted generating function for cel...

1047-3203/$ see front matter 2008 Elsevier Inc. A doi:10.1016/j.jvcir.2008.04.001 * Corresponding author. E-mail addresses: [email protected] (H. Li), k Ngan). In this paper, a novel face segmentation algorithm is proposed based on facial saliency map (FSM) for head-and-shoulder type video application. This method consists of three stages. The first stage is to generate the saliency map of in...