Download Calculus of variations and harmonic maps by Hajime Urakawa PDF

By Hajime Urakawa

This booklet presents a large view of the calculus of adaptations because it performs a necessary position in numerous parts of arithmetic and technology. Containing many examples, open difficulties, and workouts with entire recommendations, the e-book will be compatible as a textual content for graduate classes in differential geometry, partial differential equations, and variational tools. the 1st a part of the e-book is dedicated to explaining the suggestion of (infinite-dimensional) manifolds and comprises many examples. An advent to Morse thought of Banach manifolds is supplied, besides an explanation of the lifestyles of minimizing capabilities below the Palais-Smale . the second one half, that may be learn independently of the 1st, offers the speculation of harmonic maps, with a cautious calculation of the 1st and moment diversifications of the power. a number of functions of the second one edition and type theories of harmonic maps are given.

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SSR Ser. Fiz. Teklam. Mat. Nauk. (1982), 41^7. , On a theorem from linear algebra Izv.. Akad. Nauk. Modav. SSR Ser. Fiz. Teklam Mat. Nauk. (1982) 29-33. , On the theory of meromorphic curves. Dokl, Akad. Nauk. SSR (1983), 377-381. , Meromorphic mappings of a covering space 32 [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] High Points in the History of Value Distribution Theory over Cn into protective algebraic variety and defect relations, Hiroshima Math. J. 6 (1976), 265-280.

Let Sft be the field of meromorphic functions on M. Let ^ be a subfield of 3ft. The / is said to be defined over ® if and only if (£/ C ®. The meromorphic map / is said to be linearly non-degenerated over ® if and only if (/, g) is free for every meromorphic map g : M —> P(V*) defined over ®. Let © = {pj}jeQ be a finite family of meromorphic maps gj : M —> P(V*) with indeterminacy I9j. Define (109) /« Let ®© = C((£@) be the extension field of ® in M generated by (£©. The family © is said to be in general position if and only if there is a point 2 €.

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