On weakly harmonic maps from Finsler to riemannian manifolds

 Access to full text

 Full (PDF)

1. [1] Bao D., Lackey B., A Hodge decomposition theorem for Finsler spaces, C. R. Acad. Sci. Paris Ser. I Math.323 (1996) 51-56. Zbl0852.53051MR1401628
2. [2] Bao D., Chern S.S., Shen Z., An Introduction to Riemann Finsler Geometry, Graduate Texts in Mathematics, vol. 200, Springer, Berlin, Heidelberg, New York, 2000. Zbl0954.53001MR1747675
3. [3] Caffarelli L.A., Regularity theorems for weak solutions of some nonlinear systems, Comm. Pure Appl. Math.35 (1982) 833-838. Zbl0496.35035MR673831
4. [4] Centore P., Finsler Laplacians and minimal-energy maps, Internat. J. Math.11 (2000) 1-13. Zbl1110.58307MR1757888
5. [5] Eells J., Fuglede B., Harmonic Maps Between Riemannian Polyhedra, Cambridge Tracts in Mathematics, vol. 142, Cambridge University Press, Cambridge, 2001. Zbl0979.31001MR1848068
6. [6] Fuglede B., Hölder continuity of harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature, Calc. Var.16 (2003) 375-403. Zbl1025.31004MR1971035
7. [7] Fuglede B., The Dirichlet problem for harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature, Trans. AMS357 (2005) 757-792. Zbl1061.31008MR2095630
8. [8] Fuglede B., Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above, Calc. Var.31 (2008) 99-136. Zbl1133.58004MR2342616
9. [9] Giaquinta M., Hildebrandt S., A priori estimates for harmonic mappings, J. Reine Angew. Math.336 (1982) 124-164. Zbl0508.58015MR671325
10. [10] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 ed., Springer, Berlin, New York, 2001. Zbl0361.35003MR1814364
11. [11] Gromoll D., Klingenberg W., Meyer W., Riemannsche Geometrie im Großen, Lecture Notes Math., vol. 55, Springer, Berlin, Heidelberg, 1968. Zbl0293.53001
12. [12] Hildebrandt S., Kaul H., Widman K.-O., Dirichlet's boundary value problem for harmonic mappings of Riemannian manifolds, Math. Z.147 (1976) 225-236. Zbl0313.31015MR407892
13. [13] Hildebrandt S., Widman K.-O., Some regularity results for quasilinear elliptic systems of second order, Math. Z.142 (1975) 67-86. Zbl0317.35040MR377273
14. [14] Hildebrandt S., Jost J., Widman K.-O., Harmonic mappings and minimal submanifolds, Invent. Math.62 (1980/81) 269-298. Zbl0446.58006MR595589
15. [15] Hildebrandt S., Harmonic mappings of Riemannian manifolds, in: Giusti E. (Ed.), Harmonic Mappings and Minimal Immersions, Montecatini, 1984, Lecture Notes in Math., vol. 1161, Springer, Berlin, 1985, pp. 1-117. Zbl0581.58011MR821968
16. [16] Jäger W., Kaul H., Uniqueness and stability of harmonic maps and their Jacobi fields, Man. Math.28 (1979) 269-291. Zbl0413.31006MR535705
17. [17] Jost J., Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen, Manuscripta Math.32 (1989) 51-57. Zbl0455.53036MR592709
18. [18] Jost J., Equilibrium maps between metric spaces, Calc. Var.2 (1994) 173-204. Zbl0798.58021MR1385525
19. [19] Jost J., Convex functionals and generalized harmonic maps into spaces of nonpositive curvature, Comment. Math. Helv.70 (1995) 659-673. Zbl0852.58022MR1360608
20. [20] Jost J., Nonpositive Curvature: Geometric and Analytic Aspects, Birkhäuser, Basel, 1997. Zbl0896.53002MR1451625
21. [21] Jost J., Generalized Dirichlet forms and harmonic maps, Calc. Var.5 (1997) 1-19. Zbl0868.31009MR1424346
22. [22] M. Meier, On quasilinear elliptic systems with quadratic growth, Preprint SFB 72 Univ. Bonn, 1984. 
23. [23] Mo X., Harmonic maps from Finsler manifolds, Illinois J. Math.45 (2001) 1331-1345. Zbl0996.53047MR1895460
24. [24] Moser J., On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math.14 (1961) 577-591. Zbl0111.09302MR159138
25. [25] Payne L.E., Some comments on the past fifty years of isoperimetric inequalities, in: Everitt W.N. (Ed.), Inequalities – Fifty Years on from Hardy, Littlewood and Pólya, Lect. Notes Pure Appl. Math., vol. 129, Dekker, New York, Basel, Hong Kong, 1991, pp. 143-161. Zbl0723.52003MR1112577
26. [26] Pingen M., A priori estimates for harmonic mappings, Analysis27 (2007) 387-404. Zbl1145.35056MR2373663
27. [27] M. Pingen, Zur Regularitätstheorie elliptischer Systeme und harmonischer Abbildungen, Dissertation Univ. Duisburg–Essen, 2006. 
28. [28] G. Pólya, G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Ann. Math. Studies, vol. 27, 1951. Zbl0044.38301MR43486
29. [29] Shen Y., Zhang Y., Second variation of harmonic maps between Finsler manifolds, Sci. China Ser. A47 (2004) 39-51. Zbl1217.53077MR2054666
30. [30] Souza M., Spruck J., Tenenblat K., A Bernstein type theorem on a Randers space, Math. Ann.329 (2004) 291-305. Zbl1073.53014MR2060364
31. [31] Tachikawa A., A partial regularity result for harmonic maps into a Finsler manifold, Calc. Var. Partial Differential Equations16 (2003) 217-224, erratum: 225–226. Zbl1023.49032
32. [32] von der Mosel H., Winklmann S., On weakly harmonic maps from Finsler to Riemannian manifolds, Preprint 15 Institut f. Mathematik, RWTH Aachen 2006, see, http://www.instmath.rwth-aachen.de/, →preprints. Zbl1166.53050

1. Atsushi Tachikawa, Partial regularity results up to the boundary for harmonic maps into a Finsler manifold