Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 8 of 8 for “"harmonic maps"”.
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Harmonic maps of trivalent trees
This thesis is a study of harmonic maps of trivalent trees into Euclidean space. The existence of such maps is established, and uniqueness is shown to hold up to a certain isotopy condition. Moreover, within its particular isotopy class, each harmonic map is shown to be a local minimum for the …
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The evolution equations for Dirac-harmonic Maps
… thesis investigates the gradient flow of Dirac-harmonic maps. Dirac-harmonic maps are critical points of an energy functional that is motivated from supersymmetric field theories. The critical points of this energy functional couple the equation for harmonic maps with spinor fields. At present, …
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Structure of Singular Sets Local to Cylindrical Singularities for Stationary Harmonic Maps and Mean Curvature Flows
… results for the singular sets of stationary harmonic maps and mean curvature flows local to particular singularities. The original work is contained in Chapter 5 and Chapter 8. Chapters 1-5 are concerned with energy minimising maps and stationary harmonic maps. Chapters 6-8 are concerned with …
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Volume and Energy Stability for Immersions (Harmonic, Minimal)
… submanifolds of a given manifold and also on harmonic maps between manifolds. It is known, for instance, that the critical sets of the volume functional and the energy functional coincide for a Riemannian immersion f between two Riemannian manifolds.
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Sigma Models with Repulsive Potentials
<p>Motivated by questions arising in the study of harmonic maps and Yang Mills theory, we study new techniques for producing optimal monotonicity relations for geometric partial differential equations. We apply these results to sharpen epsilon regularity results. As a sample application, we analyze …
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Variational problems on supermanifolds
… of the resulting supermanifolds of fields/maps. We show that each map is uniquely characterized by a family of differential operators of appropriate order. Moreover, we demonstrate that each of this maps is uniquely characterized by its component fields, i.e. by the coefficients in a Taylor …
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Geometric quantization and dynamical constructions on the space of Kähler metrics
… the space of toric Kähler metrics there exists a harmonic map from the manifold with these boundary values and, up to the first two derivatives, it is the limit of harmonic maps from the Riemannian manifold into the spaces of Bergman metrics. This generalizes previous work of Song-Zelditch on …
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Biharmonic maps
… of the gradient flow for the (intrinsic) biharmonic energy under suitable curvature or initial energy assumptions. Moreover we use the biharmonic energy to regularize the Dirichlet energy for maps from a Riemannian surface into a round sphere. Finally we prove the so called energy identity …