Mapping properties of geometric elliptic operators in conformally conical spaces: an introduction with examples

TL;DR

This paper introduces the mapping properties of geometric elliptic operators like the Laplacian in spaces with conical singularities, illustrating their broad applicability in geometric analysis through examples.

Contribution

It provides an expository overview of the approach to elliptic operators in conical spaces, highlighting its versatility and unifying various applications.

Findings

Mapping properties of elliptic operators in conical spaces are well-understood.

The approach unifies disparate applications in geometric analysis.

Examples demonstrate the broad applicability of the theory.

Abstract

In this largely expository note, we discuss the mapping properties of the Laplacian (and other geometric elliptic operators) in spaces with an isolated conical singularity following the approach developed by B.-W. Schulze and collaborators. Our presentation aims at illustrating the versatility of these results by describing how certain representative (and seemingly disparate) applications in Geometric Analysis follow from a common setup.