Prescribed $k$-symmetric curvature hypersurfaces in de Sitter space

TL;DR

This paper proves the existence of compact spacelike hypersurfaces with prescribed k-curvature in de Sitter space, where the curvature depends on space and tilt, advancing geometric analysis in Lorentzian manifolds.

Contribution

It establishes the existence of such hypersurfaces with a new class of prescribed curvature functions depending on space and tilt.

Findings

Existence of compact spacelike hypersurfaces with prescribed k-curvature.

Curvature prescription depends on space and tilt function.

Advances in geometric analysis in de Sitter space.

Abstract

We prove existence of compact spacelike hypersurfaces with prescribed k - curvature in de Sitter space, where the prescription function depends on both space and the tilt function.