Daskalopoulos, Georgios; Mese, Chikako Harmonic maps from a simplicial complex and geometric rigidity. (English) Zbl 1142.58014 J. Differ. Geom. 78, No. 2, 269-293 (2008). The paper is concerned with harmonic maps from a flat simplicial complex (with some admissability condition) to a non-positively curved Riemannian manifold. It studies questions related to the field of rigidity theorems. One of the main tools is the Bochner technique.The theorems, stated in more general form for harmonic maps with respect to weighted energies, include: (i) Hölder continuity of the gradient away from the skeleton of codimension \(2\); (ii) a balancing condition along the skeleton of codimension \(1\); (iii) a special structure if the domain is \(2\)-dimensional: mappings restricted to \(2\)-simplexes are totally geodesic; (iv) some connections of regularity with the spectral theory of graphs. Reviewer: Andreas Gastel (Erlangen) Cited in 12 Documents MSC: 58E20 Harmonic maps, etc. 53C43 Differential geometric aspects of harmonic maps Keywords:harmonic maps; rigidity; vanishing theorems; Bochner formula PDFBibTeX XMLCite \textit{G. Daskalopoulos} and \textit{C. Mese}, J. Differ. Geom. 78, No. 2, 269--293 (2008; Zbl 1142.58014) Full Text: DOI Euclid