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Scalable Frames and Convex Geometry
Scalable frames tight frames preconditioning Farkas’s lemma
2015/12/10
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight...
Centro-Affine Invariants for Smooth Convex Bodies
Centro-Affine Invariants Smooth Convex Bodies
2010/11/24
Employing a centro-affine flow on smooth convex bodies, we generate new centro-affine differential invariants. One class of the newly defined invariants is the object of a sharp isoperimetric inequali...
Solving a long-standing open question in convex geometry, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, we use an easy curva...
McMullen's g-vector is important for simple convex polytopes. This paper postulates axioms for its extension to general convex polytopes. It also conjectures that, for each dimension d, a stated fini...
Existence and uniqueness theorem for convex polyhedral metrics on compact surfaces
uniqueness theorem convex polyhedral metrics compact surfaces
2010/11/19
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemanni...