Canonical metrics in a conformal class

TL;DR

This paper discusses the development of canonical metrics and conformal invariants for closed even-dimensional manifolds with non-degenerate conformal structures, including compact Riemann surfaces, to better understand their geometric properties.

Contribution

It introduces new canonical metrics and conformal invariants specifically tailored for non-degenerate conformal structures on closed manifolds and Riemann surfaces.

Findings

Construction of canonical metrics for conformal classes

Introduction of conformal invariants for geometric analysis

Application to compact Riemann surfaces

Abstract

Canonical metrics and conformal invariants are presented for closed oriented even-dimensional manifolds with non-degenerate conformal structures and in particular for compact Riemann surfaces.