3 papers
math.DG2024
On some relations between the Perimeter, the Area and the Visual Angle of a Convex Set
Joaquim Bruna, Julià Cufí, Agustí Reventós
We establish some relations between the perimeter, the area and the visual angle of a planar compact convex set. Our first result states that Crofton's formula is the unique univer…
math.HO2023
A historical review of the Cauchy-Riemann equations and the Cauchy Theorem
Julià Cufí, Agustí Reventós
In this article we take a historical tour through the Cauchy-Riemann equations and their relationship with Cauchy's theorem on the independence with respect to the path of the inte…
math.MG2023
On the solid angle of a convex set
J. Bruna, J. Cufí E. Gallego, A. Reventós
Here we analyze three dimensional analogues of the classical Crofton's formula for planar compact convex sets. In this formula a fundamental role is played by the visual angle of t…