Publications

2018

• On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds
  
  • Sacchelli Ludovic
  • Sigalotti Mario
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 2018. In this article we study the validity of the Whitney $C^1$ extension property for horizontal curves in sub-Riemannian manifolds endowed with 1-jets that satisfy a first-order Taylor expansion compatibility condition. We first consider the equiregular case, where we show that the extension property holds true whenever a suitable non-singularity property holds for the input-output maps on the Carnot groups obtained by nilpotent approximation. We then discuss the case of sub-Riemannian manifolds with singular points and we show that all step-2 manifolds satisfy the $C^1$ extension property. We conclude by showing that the $C^1$ extension property implies a Lusin-like approximation theorem for horizontal curves on sub-Riemannian manifolds.
• Sufficient optimality conditions for bilinear optimal control of the linear damped wave equation
  
  • Bethke Franz
  • Kröner Axel
  , 2018. In this paper we discuss sufficient optimality conditions for an optimal control problem for the linear damped wave equation with the damping parameter as the control. We address the case that the control enters quadratic in the cost function as well as the singular case that the control enters affine. For the non-singular case we consider strong and weak local minima , in the singular case we derive sufficient optimality conditions for weak local minima. Thereby, we take advantage of the Goh transformation applying techniques recently established in Aronna, Bonnans, and Kröner [Math. Program. 168(1):717–757, 2018] and [INRIA research report, 2017]. Moreover, a numerical example for the singular case is presented.
• The geometry of random minimal factorizations of a long cycle via biconditioned bitype random trees
  
  • Féray Valentin
  • Kortchemski Igor
  Annales Henri Lebesgue, UFR de Mathématiques - IRMAR, 2018, 1, pp.149-226. (10.5802/ahl.5)
  DOI : 10.5802/ahl.5
• Epidemics and the Eden model : a detailed study of robustness
  
  • Gerin Lucas
  , 2018, Emergence, Complexity and Computation, vol 27, pp.165-178. We present some well-known and less well-known properties of the Probabilistic Cellular Automaton \emph{Epidemics} on a finite grid and its analogous on the infinite square lattice: the Eden model. (10.1007/978-3-319-65558-1_12)
  DOI : 10.1007/978-3-319-65558-1_12
• Gauge-reversing maps on cones, and Hilbert and Thompson isometries
  
  • Walsh Cormac
  Geometry and Topology, Mathematical Sciences Publishers, 2018, 22 (1), pp.55-104. We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone. (10.2140/gt.2018.22.55)
  DOI : 10.2140/gt.2018.22.55