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PreprintCC BY 4.0arXiv

Canonical parameters on marginally trapped surfaces in the Minkowski 4-space

  • Miroslav Maksimović
  • Velichka Milousheva
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Abstract

Marginally trapped surfaces are spacelike surfaces in the Minkowski space whose mean curvature vector is lightlike at each point. In general, the marginally trapped surfaces are determined by seven functions satisfying several conditions (differential equations). In the present paper, we introduce special principal parameters, called canonical, and prove that every marginally trapped surface of general type admits (at least locally) canonical principal parameters which allow us to reduce the number of functions. We prove a Fundamental existence and uniqueness theorem formulated in terms of canonical parameters, which states that every marginally trapped surface of general type is determined up to a motion by three smooth functions satisfying a system of partial differential equations. The special subclass of marginally trapped surfaces with parallel mean curvature vector field is described in terms of only one differential equation. Finally, the theory is enriched with examples of marginally trapped surfaces for which canonical parameters are determined.

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Cite

BibTeXRIS
BibTeX
@misc{maksimovic2026canonical,
  title = {{Canonical parameters on marginally trapped surfaces in the Minkowski 4-space}},
  author = {Miroslav Maksimović and Velichka Milousheva},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.08367},
  eprint = {2605.08367},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.08367},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Canonical parameters on marginally trapped surfaces in the Minkowski 4-space
AU  - Miroslav Maksimović
AU  - Velichka Milousheva
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2605.08367
UR  - https://arxiv.org/abs/2605.08367
AB  - Marginally trapped surfaces are spacelike surfaces in the Minkowski space whose mean curvature vector is lightlike at each point. In general, the marginally trapped surfaces are determined by seven functions satisfying several conditions (differential equations). In the present paper, we introduce special principal parameters, called canonical, and prove that every marginally trapped surface of general type admits (at least locally) canonical principal parameters which allow us to reduce the number of functions. We prove a Fundamental existence and uniqueness theorem formulated in terms of canonical parameters, which states that every marginally trapped surface of general type is determined up to a motion by three smooth functions satisfying a system of partial differential equations. The special subclass of marginally trapped surfaces with parallel mean curvature vector field is described in terms of only one differential equation. Finally, the theory is enriched with examples of marginally trapped surfaces for which canonical parameters are determined.
ER  -