Intrinsic Differential Geometry and the Existence of Quasimeromorphic Mappings

TL;DR

This paper presents a new proof demonstrating the existence of nontrivial quasimeromorphic mappings on smooth Riemannian manifolds, relying exclusively on the manifold's intrinsic geometry.

Contribution

It introduces a novel intrinsic geometric approach to establish the existence of quasimeromorphic mappings, avoiding extrinsic methods.

Findings

Existence of nontrivial quasimeromorphic mappings on smooth Riemannian manifolds

New proof based solely on intrinsic geometry

Potential applications in geometric analysis and topology

Abstract

We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.