---
abstract: |
    Employing Morse theory and the method of analytic discs but no $\overline{ \partial}$ techniques, we establish a version of the Hartogs extension theorem in a singular setting, namely: for every domain $\Omega$ of an $(n-1)$-complete normal complex space of pure dimension $n \geqslant 2$, and for every compact set $K \subset
    \Omega$ such that $\Omega \backslash K$ is connected, holomorphic or meromorphic functions in $\Omega \backslash K$ extend holomorphically or meromorphically to $\Omega$.
address:
- ' Département de Mathématiques et Applications, UMR 8553 du CNRS, École Normale Supérieure, 45 rue d’Ulm, F-75230 Paris Cedex 05, France.  : [http://www.cmi.univ-mrs.fr/$\sim$merker/index.html]{}'
- 'Department of Engineering, Physics and Mathematics, Mid Sweden University, Campus Sundsvall, S-85170 Sundsvall, Sweden '
author:
- Joël Merker and Egmont Porten
date: '--'
title: |
     The Hartogs extension theorem\
    on $(n-1)$-complete complex spaces 
---

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**Table of contents**

[**1. Introduction 1.**]{}

[**2. Statement of the results 2.**]{}

[**3. Geometrical preparations 5.**]{}

[**4. Holomorphic extension to $D_{\rm reg}$ 10.**]{}

[**5. Meromorphic extension on nonnormal complex spaces 16.**]{}

[[**\[5 colored illustrations\]**]{}]{}

 §1. Introduction {#introduction .unnumbered}
=================

The goal of the present article is to perform a generalization of the classical Hartogs extension theorem in certain singular complex spaces 