Morse Index Stability for Sequences of Sacks-Uhlenbeck Maps into a
Sphere
Morse Index Stability for Sequences of Sacks-Uhlenbeck Maps into a
Sphere
In this paper we consider sequences of $p$-harmonic maps, $p>2$, from a closed Riemann surface $\Sigma$ into the $n$-dimensional sphere $\mathbb{S}^n$ with uniform bounded energy. These are critical points of the energy $E_p(u) :=\int_\Sigma \left( 1+|{\nabla u}|^2\right)^{p/2} \ dvol_\Sigma.$ Our two main results are an improved pointwise estimate of the …