Admissibility, Topology, and the σk-Loewner–Nirenberg Problem

Hao Fang; Matthew J Gursky

doi:10.48550/arxiv.2606.16033

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Admissibility, Topology, and the σk-Loewner–Nirenberg Problem

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Admissibility, Topology, and the σk-Loewner–Nirenberg Problem

Hao Fang and Matthew J Gursky

ArXiv.org

Cornell University

06/14/2026

DOI: 10.48550/arxiv.2606.16033

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Theσ_(k) -Loewner–Nirenberg problem is a fully nonlinear generalization of the classical Loewner–Nirenberg problem of constructing complete conformal metrics with constant negative scalar curvature in the interior of domains. For theσ_(k) -version, oncek > 1 , one must impose a negative admissibility condition to ensure ellipticity of the equation. In this note, we exhibit topological obstructions to admissibility and illustrate this with examples.

Mathematics - Analysis of PDEs

Mathematics - Differential Geometry

Details

Title: Subtitle: Admissibility, Topology, and the σk-Loewner–Nirenberg Problem
Creators: Hao Fang - University of Iowa
Matthew J Gursky - University of Notre Dame
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2606.16033
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 06/14/2026
Academic Unit: Mathematics
Record Identifier: 9985175373502771

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