Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary

TL;DR

This paper reviews conformal invariants derived from the noncommutative residue on even-dimensional manifolds without boundary and explores potential generalizations to manifolds with boundary, inspired by recent research.

Contribution

It extends the framework of conformal invariants from boundaryless manifolds to those with boundary, building on previous work and recent developments.

Findings

Review of conformal invariants from noncommutative residue

Proposed generalizations to manifolds with boundary

Connections to recent work by Yong Wang

Abstract

We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent work of Yong Wang, we also address possible generalizations of these conformal invariants to the setting of compact manifolds with boundary.