On the Morse Index of Critical Points in the Viscosity Method

TL;DR

This paper demonstrates that in viscous approximations on Finsler manifolds, one can construct critical points that meet Morse index bounds and entropy conditions, extending existing theories.

Contribution

It introduces a method to construct critical points in viscous approximations that satisfy Morse index bounds and entropy conditions on Finsler manifolds.

Findings

Critical points satisfy Morse index bounds.

Critical points meet the entropy condition.

Method applies to Finsler manifold functionals.

Abstract

We show that in viscous approximations of functionals defined on Finsler manifolds, it is possible to construct suitable sequences of critical points of these approximations satisfying the expected Morse index bounds as in Lazer-Solimini's theory, together with the entropy condition of Michael Struwe.