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Interior estimates for Hessian quotient equations
Abstract
We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator differ in degree by one or two. Counterexamples show that this degree range is optimal. The proof combines a new nonlinear comparison function, a doubling maximum principle, and a Pogorelov estimate.
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BibTeX
@misc{qiu2026interior,
title = {{Interior estimates for Hessian quotient equations}},
author = {Guohuan Qiu and Jin Yan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24549},
eprint = {2609.24549},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24549},
}
RIS
TY - UNPB
TI - Interior estimates for Hessian quotient equations
AU - Guohuan Qiu
AU - Jin Yan
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24549
UR - https://arxiv.org/abs/2609.24549
AB - We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator differ in degree by one or two. Counterexamples show that this degree range is optimal. The proof combines a new nonlinear comparison function, a doubling maximum principle, and a Pogorelov estimate.
ER -