How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax
  Remote Access

On the Singular Set of Harmonic Maps into DM-Complexes

About this Title

Georgios Daskalopoulos and Chikako Mese

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 239, Number 1129
ISBNs: 978-1-4704-1460-3 (print); 978-1-4704-2741-2 (online)
Published electronically: June 4, 2015

View full volume PDF

View other years and numbers:

Table of Contents


  • Chapter 1. Introduction
  • Chapter 2. Harmonic maps into NPC spaces and DM-complexes
  • Chapter 3. Regular and Singular points
  • Chapter 4. Metric estimates near a singular point
  • Chapter 5. Assumptions
  • Chapter 6. The Target Variation
  • Chapter 7. Lower Order Bound
  • Chapter 8. The Domain variation
  • Chapter 9. Order Function
  • Chapter 10. The Gap Theorem
  • Chapter 11. Proof of Theorems \ref MAINTHEOREM–\ref GAPTHEOREM*
  • Appendix A. Appendix 1
  • Appendix B. Appendix 2


We prove that the singular set of a harmonic map from a smooth Riemannian domain to a Riemannian DM-complex is of Hausdorff codimension at least two. We also explore monotonicity formulas and an order gap theorem for approximately harmonic maps. These regularity results have applications to rigidity problems examined in subsequent articles.

References [Enhancements On Off] (What's this?)