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PreprintCC BY 4.0arXiv

On Polynomial Complex Hessian Equations I: Non-Linear Non-Spectral Elliptic Hessian Equations on Riemannian Manifolds

  • Rémi Delloque
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Abstract

We study a general class of fully non-linear elliptic Hessian equations on compact Riemannian manifolds. In particular, we replace the standard assumption that the equation is a symmetric function of the eigenvalues of the Hessian made by Caffarelli, Nirenberg and Spruck by a weaker one. After deriving a priori estimates for solutions under suitable assumptions on the equation, we solve it with a continuity method.

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Cite

BibTeXRIS
BibTeX
@misc{delloque2026polynomial,
  title = {{On Polynomial Complex Hessian Equations I: Non-Linear Non-Spectral Elliptic Hessian Equations on Riemannian Manifolds}},
  author = {Rémi Delloque},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06529},
  eprint = {2610.06529},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06529},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On Polynomial Complex Hessian Equations I: Non-Linear Non-Spectral Elliptic Hessian Equations on Riemannian Manifolds
AU  - Rémi Delloque
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06529
UR  - https://arxiv.org/abs/2610.06529
AB  - We study a general class of fully non-linear elliptic Hessian equations on compact Riemannian manifolds. In particular, we replace the standard assumption that the equation is a symmetric function of the eigenvalues of the Hessian made by Caffarelli, Nirenberg and Spruck by a weaker one. After deriving a priori estimates for solutions under suitable assumptions on the equation, we solve it with a continuity method.
ER  -