The Secret Hyperbolic Life of Positive Scalar Curvature

TL;DR

This survey explores the connection between minimal hypersurfaces and Gromov hyperbolic spaces, providing new smoothing techniques to address hypersurface singularities in scalar curvature geometry.

Contribution

It introduces the hyperbolic unfolding correspondence, linking geometric analysis of hypersurfaces with hyperbolic spaces, enabling solutions to singularity problems in scalar curvature geometry.

Findings

Hypersurface singularities can be resolved via hyperbolic unfolding.

Smoothing schemes effectively eliminate singularities in scalar curvature contexts.

The approach bridges minimal hypersurface analysis with hyperbolic geometry.

Abstract

This survey introduces to the hyperbolic unfolding correspondence that links the geometric analysis of minimal hypersurfaces with that of Gromov hyperbolic spaces. Problems caused from hypersurface singularities oftentimes become solvable on associated Gromov hyperbolic spaces. Applied to scalar curvature geometry this yields smoothing schemes that eliminate such singularities.