Fórmulas de Minkowski e teorema de rigidez de Liebmann

Abstract

The regular surfaces are tridimensional euclidean space subsets that can be covered by applications satisfying certain properties. From these applications, we can give characteristics to these subsets, such as Gaussian Curvature and Median Curvature. A well-known subset, the sphere, is a regular surface. However, it is such a special one, as Liebmann’s Theorem tells us that the only compact connected surface that has Gaussian Curvature constant is a sphere.