We consider the second best constant in Hardy-Sobolev inequality on a Riemannian manifold. More precisely, we are interested with existence of extremal functions for this inequality. This problem was tackled by Djadli-Druet [5] Sobolev inequalities. Here, establish corresponding result singular case. In addition, perform blow-up analysis solutions equations minimizing type. yields informations ...

This work considers the problem of reconstructing a phylogenetic tree from triplet dissimilarities, which are dissimilarities defined over taxontriplets. Triplet dissimilarities are possibly the simplest generalization of pairwise dissimilarities, and were used for phylogenetic reconstructions in the past few years. We study the hardness of finding a tree best fitting a given triplet-dissimilar...