Ricci curvature and conformality of Riemannian manifolds to spheres

TL;DR

This paper establishes bounds on the first eigenvalue of the conformal Laplacian and Yamabe invariant of compact Riemannian manifolds, linking Ricci curvature and diameter conditions to conformality with spheres.

Contribution

It provides new bounds and conditions that determine when a Riemannian manifold is conformally equivalent to a sphere, based on curvature and geometric constraints.

Findings

Bounds for the first eigenvalue of the conformal Laplacian

Bounds for the Yamabe invariant

Conditions for conformality to a sphere

Abstract

In this paper we give bounds for the first eigenvalue of the conformal Laplacian and the Yamabe invariant of a compact Riemannian manifold, by using conditions on the Ricci curvature and the diameter and deduce certain conditions on the manifold to be conformal to a sphere.