Related papers: Some open problems
In this work, we utilize infinitesimal symmetries to compute Maxwell points which play a crucial role in studying sub-Riemannian control problems. By examining the infinitesimal symmetries of the geometric control problem on the SH(2)…
In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…
We present a collection of easily stated open problems in the theory of compact constant mean curvature surfaces with boundary. We also survey the current status of answering them.
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and…
This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A…
Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the…
The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
In the present text we discuss basic aspects of the Seiberg - Witten theory mainly focusing the attantion on some geometrical details which could make the introduction to the subject more illustrative. At the same time we list there natural…
Open problems from the 15th Annual ACM Symposium on Computational Geometry.
Control theory often takes the mathematical model of the to-be-control-led system for granted. In contrast, port-Hamiltonian systems theory bridges the gap between modelling and control for physical systems. It provides a unified framework…
This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…
The article surveys inverse problems related to the twisted geodesic flows on Riemannian manifolds with boundary, focusing on the generalized ray transforms, tensor tomography, and rigidity problems. The twisted geodesic flow generalizes…
In this thesis, we provide new insights into the theory of cascade feedback linearization of control systems. In particular, we present a new explicit class of cascade feedback linearizable control systems, as well as a new obstruction to…
These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
In this note we give an introduction to the topic of quantum control, explaining what its objectives are, and describing some of its limitations.
We discuss new problems in universal algebraic geometry and explain them by boolean equations.
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…