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.

This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...

We consider feasible sets given by conic constraints, where the cone defining the constraints is convex with nonempty interior. We study the case where the feasible set is not assumed to be regular in the classical sense of Robinson and obtain a constructive description of the tangent cone under a certain new second-order regularity condition. This condition contains classical regularity as a s...

The following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that is, an algebroid embedded surface admitting an equation whose roots are Puiseux power series), using a set of exponents appearing in a root of an equation. The aim is knowing to which extent the well–known results for the quasi–ordinary case can be extended to this much wider ...

To every morphism χ : L → M of differential graded Lie algebras we associate a functors of artin rings Defχ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of χ. Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanif...

In this paper we show that, if T is an area-minimizing 2-dimensional integral current with ∂T=Q〚Γ〛, where Γ a C1,α curve for α>0 and Q arbitrary integer, then has unique tangent cone at every boundary point, polynomial convergence rate. The proof simple reduction to the case Q=1, studied by Hirsch Marini (2019).

A constant angle surface in Minkowski space is a spacelike surface whose unit normal vector field makes a constant hyperbolic angle with a fixed timelike vector. In this work we study and classify these surfaces. In particular, we show that they are flat. Next we prove that a tangent developable surface (resp. cylinder, cone) is a constant angle surface if and only if the generating curve is a ...