The structure of fully nonlinear equations and its applications to prescribed problems on complete conformal metrics
Analysis of PDEs
2025-03-25 v1 Differential Geometry
Abstract
This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory techniques to construct admissible metrics under a weak condition on the underlying metric, which can be further relaxed in a broad setting. Furthermore, we provide some topological obstruction to demonstrate the optimality of our structural conditions.
Keywords
Cite
@article{arxiv.2503.18757,
title = {The structure of fully nonlinear equations and its applications to prescribed problems on complete conformal metrics},
author = {Rirong Yuan},
journal= {arXiv preprint arXiv:2503.18757},
year = {2025}
}
Comments
This manuscript combines and extends arXiv:2011.08580, arXiv:2203.13212 and arXiv:2304.12835, with improved structural conditions and stronger results. It replaces the previous versions