Contributions to max–min convex geometry. I: Segments

Contributions to differential geometry of spacelike curves in Lorentzian plane L2

‎In this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in Lorentzian plane $mathbb{L}^{2}.$ Then the‎ ‎special curves mentioned above are studied in Lorentzian plane $mathbb{L}%‎‎^{2}.$ Finally some characterizations of these special curves are given in‎ ‎$mathbb{L}^{2}.$‎

Convex Geometry of Orbits

We study metric properties of convex bodies B and their polars B, where B is the convex hull of an orbit under the action of a compact group G. Examples include the Traveling Salesman Polytope in polyhedral combinatorics (G = Sn, the symmetric group), the set of nonnegative polynomials in real algebraic geometry (G = SO(n), the special orthogonal group), and the convex hull of the Grassmannian ...

Convex and Discrete Geometry

Geir Agnarsson, Jill Bigley Dunham.* George Mason University, Fairfax, VA. Extremal coin graphs in the Euclidean plane. A coin graph is a simple geometric intersection graph where the vertices are represented by non-overlapping closed disks in the Euclidean plane and where two vertices are connected if their corresponding disks touch. The problem of determining the maximum number of edges of a ...

Math 341: Convex Geometry

Some Results on Convex Spectral Functions: I

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...