Geometry of a class of φ-minimal surfaces in ℍ²× ℝ

@misc{freitas2026geometry,
  title = {{Geometry of a class of $φ$-minimal surfaces in $\mathbbH^2\times \mathbbR$}},
  author = {Katianny Rosa Freitas and João Paulo dos Santos and António Martínez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27187},
  eprint = {2610.27187},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27187},
}

TY  - UNPB
TI  - Geometry of a class of φ-minimal surfaces in ℍ^2× ℝ
AU  - Katianny Rosa Freitas
AU  - João Paulo dos Santos
AU  - António Martínez
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27187
UR  - https://arxiv.org/abs/2610.27187
AB  - We study a class of φ-minimal surfaces in the product space ℍ^2×ℝ, that is, weighted minimal surfaces whose corresponding weight is determined by a smooth potential function φ that depends only on the height coordinate relative to the factor ℝ. Under monotonicity, concavity, and asymptotic conditions on φ, we obtain a complete classification of connected, properly embedded φ-minimal surfaces that are invariant under isometries of ℍ^2×ℝ acting trivially on ℝ and by rotations or parabolic translations on ℍ^2. Finally, we establish several non-existence results for φ-minimal surfaces in ℍ^2 × ℝ, either by using properties of the height function or by applying the tangency principle together with suitable invariant surfaces as barriers.
ER  -