Title: Morse Index Stability of Willmore Immersions I Authors: Alexis Michelat and Tristan Rivi\`ere Categories: math.DG math.AP Comments: 96 pages MSC-class: 35J35, 35J48, 35R01, 49Q10, 53A05, 53A10, 53A30, 53C42 \\ In a recent work, F. Da Lio, M. Gianocca, and T. Rivi\`ere developped a new method to show upper semi-continuity results in geometric analysis, which they applied to conformally invariant Lagrangians in dimension $2$ (that include harmonic maps). In this article, we apply this method to show that the sum … Continue reading “Morse Index Stability of Willmore Immersions I”