Monomialization of singular metrics on real surfaces

TL;DR

This paper proves a monomialization result for real analytic tensor fields on surfaces and applies it to extend the inner metric of a resolved surface, confirming a key property at all points.

Contribution

It introduces a monomialization technique for real analytic tensor fields and applies it to singular surface metrics, extending the inner metric across resolutions.

Findings

Monomialization of tensor fields on real surfaces achieved.

Extension of inner metrics on resolved surfaces demonstrated.

Recovery of Hsiang & Pati property at all points.

Abstract

We present here a result of Monomialization of real analytic two-symmetric tensor fields over regular real analytic surfaces. We apply it to the (extension of the pull-back of the) inner metric of a resolved surface of a real analytic surface singularity. Doing so we recover Hsiang & Pati property at each point of the resolved surface.