Sharp stability for mixed bubbles on hyperbolic space

@misc{wei2026sharp,
  title = {{Sharp stability for mixed bubbles on hyperbolic space}},
  author = {Juncheng Wei and Zetian Yan and Zhipeng Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15920},
  eprint = {2610.15920},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15920},
}

TY  - UNPB
TI  - Sharp stability for mixed bubbles on hyperbolic space
AU  - Juncheng Wei
AU  - Zetian Yan
AU  - Zhipeng Yang
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15920
UR  - https://arxiv.org/abs/2610.15920
AB  - We prove sharp residual stability estimates for the critical Poincaré-Sobolev equation near sums of one positive hyperbolic solution and one projected Euclidean bubble in dimensions at least four. The estimates are uniform in the relative positions of the centers. The sharp rate is linear except in dimension six, where it contains a square root of a logarithm. For nonnegative functions, the same estimates hold under an energy constraint near the sum of the two profile energies for λ outside a finite set, and an additional mass constraint removes this restriction. For arbitrary finite numbers of profiles, we identify and realize all nonnegative Palais-Smale levels. We characterize the parameters at which different pairs of profile numbers have the same energy and show that the limiting energy and mass determine both profile numbers.
ER  -