Relations between threshold constants for Yamabe type bordism invariants

TL;DR

This paper investigates the threshold constants for Yamabe type bordism invariants, providing variational characterizations and explicit bounds, advancing understanding of geometric invariants in differential geometry.

Contribution

It introduces variational characterizations of threshold constants and establishes an explicit positive lower bound for spinorial threshold constants.

Findings

Threshold constants are characterized via Yamabe-type equations.

A positive lower bound for spinorial threshold constants is derived.

The results deepen understanding of bordism invariants in geometric analysis.

Abstract

In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants are characterized through Yamabe-type equations on products of spheres with rescaled hyperbolic spaces. We give variational characterizations of these threshold constants, and our investigations lead to an explicit positive lower bound for the spinorial threshold constants.