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.
Dominik Schlagenhauf (Tue,) studied this question.