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Furthering the development of Da Lio-Gianocca-Rivi\`ere's Morse stabilitytheory (arXiv:2212.03124) that was first applied to harmonic maps betweenmanifolds and later extended to the case of Willmore immersions(arXiv:2306.04608-04609), we generalise the method to the case of (intrinsic orextrinsic) biharmonic maps. In the course of the proof, we develop a novelmethod to prove strong energy quantization (in the space of squared-integrablefunctions that corresponds to the pre-dual of the Marcinkiewicz space of weaklysquared-integrable functions) in a wide class of problems in geometricanalysis, which allows us to recover some previous results in a unifiedfashion.

Morse Index Stability of Biharmonic Maps in Critical Dimension