No description available.

by Lam Kwan Hang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 75-76). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Maps into locally compact Riemannian complex --- p.8 / Chapter 2.1 --- Exitsence of energy minimizing maps --- p.8 / Chapter 2.2 --- Length minimizing curves --- p.10 / Chapter 3 --- Harmonic maps into nonpositively curved spaces --- p.13 / Chapter 3.1 --- Nonpositively curved spaces --- p.13 / Chapter 3.2 --- Properties of the distance function --- p.16 / Chapter 4 --- Basic properties of harmonic maps into NPC spaces --- p.21 / Chapter 4.1 --- Monotonicity formula --- p.21 / Chapter 4.2 --- Approximately differentiable maps --- p.24 / Chapter 4.3 --- Local properties of harmonic maps --- p.28 / Chapter 5 --- Existence and uniqueness of harmonic maps in a ho- motopy class --- p.33 / Chapter 5.1 --- Convexity properties of the energy functional --- p.33 / Chapter 5.2 --- Existence and Uniqueness Theorem --- p.37 / Chapter 6 --- Homogeneous approximating maps --- p.40 / Chapter 6.1 --- Regular homogeneous map --- p.40 / Chapter 6.2 --- Homogeneous approximating map --- p.46 / Chapter 7 --- More results on regularity --- p.52 / Chapter 7.1 --- Intrinsically differentiable maps --- p.52 / Chapter 7.2 --- Good homogeneous approximating map --- p.62 / Chapter 8 --- Harmonic maps into building-like complexes --- p.65 / Chapter 8.1 --- F-connected complex --- p.65 / Chapter 8.2 --- Regularity and the Bochner technique --- p.66 / Bibliography --- p.75

Academisch proefschrift--Vrije Universiteit, Amsterdam. / "Stellingen": [2] p. laid in. Bibliography: p. 20-21.

No description available.

No description available.

No description available.

Thesis (PH. D.) - University of Michigan, 1940. / Reprinted from Annals of mathematics, vol. 42, no. 1, January, 1941. Bibliography: p. 246.

Academisch proefschrift--Vrije Universiteit, Amsterdam. / "Stellingen": [2] p. laid in. Bibliography: p. 20-21.

Thesis--University of Kansas. / Includes bibliographical references.

Certain properties of the solution u of the equation Pu = v in a Banach space will be investigated. It will be assumed that v is a prescribed element of the space, P is a transformation defined on a closed subset in the space and consisting of the sum of a linear transformation and a contraction mapping, and that P and v depend on a real variable λ. which assumes values over the half-open positive interval 0 < λ ≤ λₒ. Then a theorem will be proved, establishing the existence and uniqueness of the solution u(λ) of P(λ)u(λ) = v(λ) . Under the hypothesis that P and v possess asymptotic expansions as λ→0, it will be shown that asymptotic solutions exist, that they are asymptotically unique, and that they possess asymptotic expansions which may be determined by a recursive process from those of P and v. The results obtained will be applied to particular types of Banach spaces, such as finite-dimensional Euclidean spaces, spaces of Lebesgue-square-summable functions and of continuous functions over a closed interval. / Science, Faculty of / Mathematics, Department of / Graduate