The conformal Yamabe constant of product manifolds

TL;DR

This paper establishes a lower bound for the conformal Yamabe constant of product manifolds based on the constants of the individual factors, advancing understanding in geometric analysis.

Contribution

It provides a new inequality relating the conformal Yamabe constants of product manifolds to those of their factors.

Findings

Derived a lower bound for the conformal Yamabe constant of product manifolds.

Connected the conformal Yamabe constants of product manifolds to those of component manifolds.

Enhanced tools for analyzing scalar curvature in geometric analysis.

Abstract

Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h).