Antoine and Zouaki ([1] and [16]) have given the existence of a continuous selection of (1.1) in the particular case where M − x0 and N − y0 are closed convex cones . In this paper, we extend this result when M (resp. N) approximates continuously its Clarke tangent cone at x0 (resp. y0) (see Definition 2.2). This property is verified at x0 for an important class of sets. We get among others: se...

We analyze the properties of an interior point cutting plane algorithm that is based on a semi-infinite linear formulation of the dual semidefinite program. The cutting plane algorithm approximately solves a linear relaxation of the dual semidefinite program in every iteration and relies on a separation oracle that returns linear cutting planes. We show that the complexity of a variant of the i...

We investigate the local deformation space of 3-dimensional conemanifold structures of constant curvature κ ∈ {−1, 0, 1} and coneangles≤ π. Under this assumption on the cone-angles the singular locus will be a trivalent graph. In the hyperbolic and the spherical case our main result is a vanishing theorem for the first Lcohomology group of the smooth part of the cone-manifold with coefficients ...

We present an explicit minimal set of generators for the defining ideal family Backelin semigroups and find its Betti numbers. In particular, we compute type semigroup as well, correcting a claim in literature. Additionally, show that numbers corresponding numerical ring coincide to those tangent cone.

We give a natural way to identify between two scales, potentially arbitrarily far apart, in non-compact Ricci-flat manifold with Euclidean volume growth when tangent cone at infinity has smooth cross section. The identification map is given as the gradient flow of solution an elliptic equation.

We consider a novel curvature flow for curves on the 2-dimensional light cone, contained in 3-dimensional Minkowski space. show that solutions to (CF) such are correspondence with inverse (ICF). prove ellipses and hyperbolas only evolve under homotheties. The closed ones they ancient solutions. spacelike curve cone is self-similar solution CF (resp. (ICF)) if, its of curvature) differs by const...

We characterise equality cases in matrix H¨older’s inequality and develop a divergence formulation of optimal transport vector measures. As an application, we reprove the representation formula for measures polar cone to monotone maps. generalise last result wide class of cones, including cones tangent unit ball space differentiable functions Sobolev spaces.