The Equivariant Second Yamabe Constant

TL;DR

This paper introduces the $G$-equivariant second Yamabe constant for closed Riemannian manifolds and investigates the existence of $G$-invariant nodal solutions to the Yamabe equation, extending understanding of symmetry in geometric analysis.

Contribution

It defines the $G$-equivariant second Yamabe constant and provides new results on the existence of $G$-invariant nodal solutions, linking symmetry groups to solutions of the Yamabe problem.

Findings

Existence of $G$-invariant nodal solutions established.

Introduction of the $G$-equivariant second Yamabe constant.

Results extend symmetry considerations in the Yamabe problem.

Abstract

For a closed Riemannian manifold of dimension $n\geq 3$ and a subgroup $G$ of the isometry group, we define and study the $G-$equivariant second Yamabe constant and we obtain some results on the existence of $G-$invariant nodal solutions of the Yamabe equation.