13 citations · 18 across the 2 of their papers we have counts for
6 papers
On the Minkowski deficit for surfaces of revolution
Joaquim Bruna, Julià Cufí, Agustí Reventós
By studying the classical Minkowski's inequality, , relating area and mean curvature, in the particular case of convex surfaces of revolution, one is led to a functi…
Integral Geometry of pairs of planes
Julià Cufí, Eduardo Gallego, Agustí Reventós
We deal with integrals of invariant measures of pairs of planes in euclidean space as considered by Hug and Schneider. In this paper we express some of these integra…
Integral Geometry about the visual angle of a convex set
Julià Cufí, Eduardo Gallego, Agustí Reventós
In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. T…
A note on Hurwitz's inequality
Julià Cufí, Eduardo Gallego, Agustí Reventós
Given a simple closed plane curve of length enclosing a compact convex set of area , Hurwitz found an upper bound for the isoperimetric deficit, namely $L^2-4πF\leq…
A lower bound for the isoperimetric deficit
Julià Cufí, Agustí Reventós
In this paper we provide a Bonnesen-style inequality which gives a lower bound for the isoperimetric deficit corresponding to a closed convex curve in terms of some geometrical inv…
Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature
Julià Cufí, Agustí Reventós
We relate the total curvature and the isoperimetric deficit of a curve in a two-dimensional space of constant curvature with the area enclosed by the evolute of . We provide…