Skip to content
DraconiticResearch
Search Sources API
178,970 studies31 sourcesUpdated 49 min ago
PreprintCC BY-NC-ND 4.0arXiv

Neumann problem for Hessian equation and geometric inequalities in hyperbolic space

  • Liangjun Weng
Open at sourcePDFDOICite

Abstract

We establish the existence of solutions to the Neumann problem for the Hessian equation on a smooth, bounded strictly static convex domain in hyperbolic space. The boundary condition determines a unique compatibility constant, and admissible solutions are unique up to a multiple of the static potential. As an application, we give a direct analytic proof of some weighted geometric inequalities for the static convex domain in hyperbolic space.

Related

  1. Classification of solutions to the Liouville equation with a nonlinear Neumann boundary condition and applications to sharp inequalities
    Xiaohan Cai, Abdolhakim Shouman
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Inequalities for radial solutions to the wave equation on the hyperbolic space
    Peng Chen, Xuan Thinh Duong, Yunxiang Wang +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay
    Deeksha Tomer
    arXivPreprintarXiv licenceFull textAnalysis & PDEsNumerical analysis & scientific computingarXiv
  4. Global recovery of Lorentzian principal geometry from the hyperbolic Dirichlet-to-Neumann map
    Lu Chen, Yan Jiang, Hongyu Liu +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Inequalities between Dirichlet and Neumann eigenvalues in large dimensions
    N. Filonov
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{weng2026neumann,
  title = {{Neumann problem for Hessian equation and geometric inequalities in hyperbolic space}},
  author = {Liangjun Weng},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03206},
  eprint = {2611.03206},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03206},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Neumann problem for Hessian equation and geometric inequalities in hyperbolic space
AU  - Liangjun Weng
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03206
UR  - https://arxiv.org/abs/2611.03206
AB  - We establish the existence of solutions to the Neumann problem for the Hessian equation on a smooth, bounded strictly static convex domain in hyperbolic space. The boundary condition determines a unique compatibility constant, and admissible solutions are unique up to a multiple of the static potential. As an application, we give a direct analytic proof of some weighted geometric inequalities for the static convex domain in hyperbolic space.
ER  -