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PreprintCC BY 4.0arXiv

The symmetric maximal surface equation

  • Rongli Huang
  • Peihe Wang
  • Hengyu Zhou
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Abstract

We establish the existence of smooth solutions to the symmetric maximal surface equation with degenerate boundary conditions. Moreover, we prove that these solutions maximize the associated area functionals. This result serves as the Lorentzian analogue of minimal graphs in hyperbolic spaces together with their associated area minimizing problem.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026symmetric,
  title = {{The symmetric maximal surface equation}},
  author = {Rongli Huang and Peihe Wang and Hengyu Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30167},
  eprint = {2608.30167},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30167},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The symmetric maximal surface equation
AU  - Rongli Huang
AU  - Peihe Wang
AU  - Hengyu Zhou
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30167
UR  - https://arxiv.org/abs/2608.30167
AB  - We establish the existence of smooth solutions to the symmetric maximal surface equation with degenerate boundary conditions. Moreover, we prove that these solutions maximize the associated area functionals. This result serves as the Lorentzian analogue of minimal graphs in hyperbolic spaces together with their associated area minimizing problem.
ER  -