On Bifurcation of Solutions of the Yamabe Problem in Product Manifolds with Minimal Boundary

TL;DR

This paper investigates the multiplicity of solutions to the Yamabe problem on product manifolds with minimal boundary using bifurcation theory, aiming to understand solution behavior and bifurcation points.

Contribution

It introduces a bifurcation approach to analyze solution multiplicity for the Yamabe problem on manifolds with boundary, extending previous results to product manifolds.

Findings

Identification of bifurcation points for solutions

Demonstration of multiple solutions existing under certain conditions

Extension of Yamabe problem analysis to manifolds with minimal boundary

Abstract

In this paper, we study multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.