The scalar curvature in wedge spaces: existence and obstructions

TL;DR

This paper investigates the existence and obstructions to scalar curvature metrics on wedge spaces with singularities, extending previous work on conical singularities using advanced geometric analysis tools.

Contribution

It provides new existence and obstruction results for scalar curvature metrics on wedge spaces with a single singular stratum, building on established elliptic and index theories.

Findings

Existence results for scalar curvature metrics under positivity conditions

Obstructions identified for certain wedge space geometries

Extension of previous conical singularity results to wedge spaces

Abstract

We study the scalar curvature of incomplete wedge metrics in certain stratified spaces with a single singular stratum (wedge spaces). Building upon several well established technical tools for this category of spaces (the corresponding Yamabe, elliptic and index theories) we provide existence and obstruction results for such metrics under suitable positivity assumptions on the underlying geometry. This is meant to be a follow-up to a previous paper of ours (AGAG, 2022), where the case of spaces with an isolated conical singularity was considered.