Compactness results for immersions of prescribed Gaussian curvature I - analytic aspects

TL;DR

This paper extends existing mathematical results to prove the existence of hypersurfaces with constant Gaussian curvature in Hadamard manifolds, focusing on analytic methods.

Contribution

It provides new existence theorems for prescribed Gaussian curvature hypersurfaces in Hadamard manifolds, building on recent work by Guan and Spruck.

Findings

Proved existence of constant Gaussian curvature hypersurfaces in Hadamard manifolds.

Extended previous results using analytic techniques.

Contributed to the mathematical understanding of curvature-prescribed immersions.

Abstract

We extend recent results of Guan and Spruck, proving existence results for constant Gaussian curvature hypersurfaces in Hadamard manifolds.