Uhlenbeck, K. Morse theory by perturbation methods with applications to harmonic maps. (English) Zbl 0509.58012 Trans. Am. Math. Soc. 267, 569-583 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 15 Documents MSC: 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 58E20 Harmonic maps, etc. 53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) Keywords:Palais-Smale Morse theory; variational problems; Sobolev space of mappings; energy integral; Riemannian sectional curvatures Citations:Zbl 0119.092; Zbl 0122.401; Zbl 0208.128; Zbl 0372.35030 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Shmuel Agmon, The \?_{\?} approach to the Dirichlet problem. I. Regularity theorems, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 405 – 448. · Zbl 0093.10601 [2] James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109 – 160. · Zbl 0122.40102 · doi:10.2307/2373037 [3] Richard S. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Mathematics, Vol. 471, Springer-Verlag, Berlin-New York, 1975. · Zbl 0308.35003 [4] Philip Hartman, On homotopic harmonic maps, Canad. J. Math. 19 (1967), 673 – 687. · Zbl 0148.42404 · doi:10.4153/CJM-1967-062-6 [5] Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0142.38701 [6] Jürgen Moser, A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. 13 (1960), 457 – 468. · Zbl 0111.09301 · doi:10.1002/cpa.3160130308 [7] Richard S. Palais, Homotopy theory of infinite dimensional manifolds, Topology 5 (1966), 1 – 16. · Zbl 0138.18302 · doi:10.1016/0040-9383(66)90002-4 [8] Richard S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299 – 340. · Zbl 0122.10702 · doi:10.1016/0040-9383(63)90013-2 [9] R. S. Palais and S. Smale, A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165 – 172. · Zbl 0119.09201 [10] Richard S. Palais, Lusternik-Schnirelman theory on Banach manifolds, Topology 5 (1966), 115 – 132. · Zbl 0143.35203 · doi:10.1016/0040-9383(66)90013-9 [11] Richard S. Palais, Foundations of global non-linear analysis, W. A. Benjamin, Inc., New York-Amsterdam, 1968. · Zbl 0164.11102 [12] Jacob T. Schwartz, Generalizing the Lusternik-Schnirelman theory of critical points, Comm. Pure Appl. Math. 17 (1964), 307 – 315. · Zbl 0152.40801 · doi:10.1002/cpa.3160170304 [13] S. Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. of Math. (2) 80 (1964), 382 – 396. · Zbl 0131.32305 · doi:10.2307/1970398 [14] A. J. Tromba, A general approach to Morse theory, J. Differential Geometry 12 (1977), no. 1, 47 – 85. · Zbl 0344.58012 [15] K. Uhlenbeck, Morse theory on Banach manifolds, J. Functional Analysis 10 (1972), 430 – 445. · Zbl 0241.58002 [16] K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), no. 3-4, 219 – 240. · Zbl 0372.35030 · doi:10.1007/BF02392316 [17] K. Uhlenbeck, Harmonic maps; a direct method in the calculus of variations, Bull. Amer. Math. Soc. 76 (1970), 1082 – 1087. · Zbl 0208.12802 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.