A proof of the Kazdan-Warner identity via the Minkowski spacetime

TL;DR

This paper presents a novel proof of the Kazdan-Warner identity by embedding 2D spherical manifolds into Minkowski spacetime lightcones, linking geometric analysis with spacetime embeddings.

Contribution

It introduces a new proof technique for the Kazdan-Warner identity using isometric embeddings into Minkowski spacetime lightcones.

Findings

Proof of the Kazdan-Warner identity via spacetime embedding

Establishment of isometric embedding of spherical manifolds into Minkowski lightcones

Connection between geometric analysis and spacetime geometry

Abstract

Any 2-dim Riemannian manifold with spherical topology can be embedded isometrically into a lightcone of the Minkowski spacetime. We apply this fact to give a proof of the Kazdan-Warner identity.