Stability of the morse index for the p-harmonic approximation of harmonic maps into homogeneous spaces

Abstract In the joint work of the author with Da Lio, F. , and Rivière, T. , Schlagenhauf, D.: (2025) we studied the stability of the Morse index for Sacks-Uhlenbeck sequences into spheres as p 2 p ↘ 2. These are critical points of the energy Eₚ (u): = _ (1+| u| ²) ^p/2 \ dvol_, E p (u): = ∫ Σ 1 + ∇ u 2 p / 2 d v o l Σ, where u: Sⁿ u: Σ → S n is a map from a closed Riemannian surface Σ into a sphere Sⁿ S n. In this paper we extend the results found in Da Lio, F. , Rivière, T. , Schlagenhauf, D.: (2025) to the case of Sacks-Uhlenbeck sequences into homogeneous spaces, by incorporating the strategy introduced in Bayer, C. , and Roberts, A.: (2025). In the spirit of Da Lio, F. , Rivière, T. , Schlagenhauf, D.: (2025), we show in this setting the upper semicontinuity of the Morse index plus nullity and an improved pointwise estimate of the gradient in the neck regions around blow up points.