Erratum to: Quotient metrics with applications in convex geometry

Recurrent metrics in the geometry of second order differential equations

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

Applications of Convex and Algebraic Geometry to Graphs

Applications of Convex and Algebraic Geometry to Graphs and Polytopes

Geometry of splice-quotient singularities

We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate functions. The elegant way is the language of of line bundles based on Okuma’s description of the function ring of the universal abelian cover. As an easy applicat...

Harmonic Symmetrization of Convex Sets and of Finsler Structures, with Applications to Hilbert Geometry

David Hilbert discovered in 1895 an important metric that is canonically associated to an arbitrary convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof of this fact assumes a certain degree of smoothness of the boundary of Ω, and refers to a theorem by Busemann and Mayer that produces the norm of a tangent vector from the distance f...