Morse index of min-max stationary integral varifolds

TL;DR

This paper establishes an upper bound on the Morse index of certain minimal varifolds that arise from min-max methods, linking geometric variational properties to topological invariants.

Contribution

It provides a new upper bound for the Morse index of min-max stationary integral varifolds associated with the $d$-dimensional $p$-width of closed Riemannian manifolds.

Findings

Upper bound for Morse index of min-max stationary varifolds

Connection between Morse index and $p$-width

Advances understanding of stability in geometric variational problems

Abstract

We prove an upper bound for the Morse index of min-max stationary integral varifolds realizing the $d$-dimensional $p$-width of a closed Riemannian manifold.