Hessian estimates for the sigma-2 equation in dimension four
We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher $(n\ge 5)$ dimensions.
Authors
- Ravi Shankar (ORCID: https://orcid.org/0000-0001-8724-593X)
- Yu Yuan (ORCID: https://orcid.org/0000-0001-5004-910X)
Institutions
- Princeton University (US)
- University of Washington (US)
Publication Details
- Journal
- Annals of Mathematics
- Published
- 2025-03-01
- DOI
- https://doi.org/10.4007/annals.2025.201.2.4
- Citations
- 7
- Primary Topic
- Advanced Mathematical Physics Problems
- Type
- article
- Field-Weighted Citation Impact
- 25.85