11 papers
Null fluid gravitational fields on Kerr manifolds and optical lifts of Sasaki structures
Masoud Ganji, Cristina Giannotti, Andrea Spiro
Building on the characterisation in [C. D. Hill, J. Lewandowski and P. Nurowski, Indiana Univ. Math. J. 57 (2008), 3131--3176] of 4-dimensional Lorentzian metrics adapted to an opt…
Black holes and black regions, horizons and barriers in Lorentzian manifolds
Cristina Giannotti, Andrea Spiro
We prove that if S is a time-oriented null hypersurface of a Lorentzian n-manifold (M, g), the causal world-lines, which intersect transversally S and are time-oriented in a compat…
Flows of vector fields and the Kalman Theorem
Fabio Bagagiolo, Cristina Giannotti, Andrea Spiro +1
We give two proofs of the Kalman Theorem, alternative to the most common ones, which infer such a classical result of Control Theory using just very basic facts on flows of vector…
Einstein manifolds with optical geometries of Kerr type
Masoud Ganji, Cristina Giannotti, Gerd Schmalz +1
We classify the Ricci flat Lorentzian -manifolds satisfying three particular conditions, encoding and combining some crucial features of the Kerr metrics and the Robinson-Trautm…
Distributions and controllability problems (II)
Cristina Giannotti, Andrea Spiro, Marta Zoppello
In [C. Giannotti, A. Spiro, M. Zoppello, {\it Distributions and controllability problems (I)}, preprint posted on ArXiv (2024)], we introduced a new approach to the real analytic n…
Distributions and controllability problems (I)
Cristina Giannotti, Andrea Spiro, Marta Zoppello
We consider a non-linear real analytic control system of first order , with controls in a connected open set …
Proving the Chow-Rashevskii Theorem à la Rashevskii
Cristina Giannotti, Andrea Spiro, Marta Zoppello
We give a new independent proof of a generalised version of the theorem by Rashevskii, which appeared in [Uch. Zapiski Ped. Inst. K. 2 (1938), 83 -- 94] and from which the classica…
On the Pontryagin Maximum Principle under differential constraints of higher order
Franco Cardin, Cristina Giannotti, Andrea Spiro
Exploiting our previous results on higher order controlled Lagrangians in [Nonlinear Anal. {\bf 207} (2021), 112263], we derive here an analogue of the classical first order Pontry…
Control problems with differential constraints of higher order
Franco Cardin, Cristina Giannotti, Andrea Spiro
We consider cost minimising control problems, in which the dynamical system is constrained by higher order differential equations of Euler-Lagrange type. Following ideas from a pre…
On the singular loci and the images of proper holomorphic maps from pseudoellipsoids
Cristina Giannotti, Andrea Spiro
We prove a generalisation of Rudin's theorem on proper holomorphic maps from the unit ball to the case of proper holomorphic maps from pseudoellipsoids.
Steepest descent curves of convex functions on surfaces of constant curvature
Cristina Giannotti, Andrea Spiro
Let S be a complete surface of constant curvature K = + 1 or -1, i.e. the sphere S^2 or the Lobachevskij plane L^2, and D a bounded convex subset of S. If S = S^2, assume also diam…