Morse Index Stability of Biharmonic Maps in Critical Dimension

Autor:	Michelat, Alexis
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry 31B30 (primary) 35J35 35J48 49Q10 53A05 (secondary)
Druh dokumentu:	Working Paper
Popis:	Furthering the development of Da Lio-Gianocca-Rivi\`ere's Morse stability theory (arXiv:2212.03124) that was first applied to harmonic maps between manifolds and later extended to the case of Willmore immersions (arXiv:2306.04608-04609), we generalise the method to the case of (intrinsic or extrinsic) biharmonic maps. In the course of the proof, we develop a novel method to prove strong energy quantization (in the space of squared-integrable functions that corresponds to the pre-dual of the Marcinkiewicz space of weakly squared-integrable functions) in a wide class of problems in geometric analysis, which allows us to recover some previous results in a unified fashion. Comment: 106 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.07494 Zobrazit plný text záznamu View this record from Arxiv