Boundary geometry and concentration points for attractive Bose-Einstein condensates with a ring-shaped potential

@misc{yu2026boundary,
  title = {{Boundary geometry and concentration points for attractive Bose-Einstein condensates with a ring-shaped potential}},
  author = {Shubin Yu and Chun-Lei Tang and Ziheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21994},
  eprint = {2610.21994},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21994},
}

TY  - UNPB
TI  - Boundary geometry and concentration points for attractive Bose-Einstein condensates with a ring-shaped potential
AU  - Shubin Yu
AU  - Chun-Lei Tang
AU  - Ziheng Zhang
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21994
UR  - https://arxiv.org/abs/2610.21994
AB  - In this paper, we study the ground states of attractive Bose-Einstein condensates in a bounded domain Ω⊂ ℝ^2 under the ring-shaped trapping potential V(x)=(|x|−1)^2. The boundary geometry of Ω may allow the ring Γ={x∈ℝ^2:|x|=1} of global minima for V(x) to meet both the interior and the boundary of Ω. As the interaction strength approaches the critical value, we prove that if Γ∩ Ωnot=∅, the mass of ground states concentrates at a point x_0∈Γ∩ Ω that has maximal distance from ∂Ω. Our method relies on exponential upper and lower bounds for the difference between the bounded domain and whole space minimal energies. The essential lower bound follows from a uniform quadratic-growth estimate near the ground state manifold of the whole space problem, which is established by combining the nondegeneracy of the optimizer for the Gagliardo-Nirenberg inequality with a Lyapunov-Schmidt reduction.
ER  -