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On the Singular Set of Harmonic Maps into DM-Complexes
About this Title
Georgios Daskalopoulos, Department of Mathematics, Brown University, Providence, Rhode Island 02904 and Chikako Mese, Department of Mathematics, Johns Hopkins University
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)
DOI: https://doi.org/10.1090/memo/1129
Published electronically: June 4, 2015
MSC: Primary 53C43, 58E20
Table of Contents
Chapters
- 1. Introduction
- 2. Harmonic maps into NPC spaces and DM-complexes
- 3. Regular and Singular points
- 4. Metric estimates near a singular point
- 5. Assumptions
- 6. The Target Variation
- 7. Lower Order Bound
- 8. The Domain variation
- 9. Order Function
- 10. The Gap Theorem
- 11. Proof of Theorems –
- A. Appendix 1
- B. Appendix 2
Abstract
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.- Georgios Daskalopoulos and Chikako Mese, Harmonic maps between singular spaces I, Comm. Anal. Geom. 18 (2010), no. 2, 257–337. MR 2672235, DOI 10.4310/CAG.2010.v18.n2.a2
- Georgios Daskalopoulos, Chikako Mese, and Alina Vdovina, Superrigidity of hyperbolic buildings, Geom. Funct. Anal. 21 (2011), no. 4, 905–919. MR 2827014, DOI 10.1007/s00039-011-0124-9
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