Structure Theorem for Riemannian surfaces with arbitrary curvature

TL;DR

This paper proves that any Riemannian surface, regardless of curvature, can be decomposed into fundamental geometric blocks such as generalized Y-pieces, funnels, and halfplanes, extending classical surface decomposition results.

Contribution

It introduces a universal decomposition theorem for Riemannian surfaces with arbitrary curvature, broadening the scope of surface topology and geometry analysis.

Findings

Decomposition into generalized Y-pieces, funnels, and halfplanes

Applicable to surfaces with any curvature

Extends classical surface decomposition results

Abstract

In this paper we prove that any Riemannian surface, with no restriction of curvature at all, can be decomposed into blocks belonging just to some of these types: generalized Y-pieces, generalized funnels and halfplanes.