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 20 of 41 for “"minimal surfaces"”.
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Min-max minimal surfaces in 3-manifolds
… sequence converging as varifolds to a smooth minimal surface (possibly disconnected, and with multiplicities). We prove a conjecture of Pitts-Rubinstein about how such a min-max sequence can degenerate; namely we show that after doing finitely many disk surgeries and isotopies on the sequence, …
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Schwarz's surface and the theory of minimal surfaces
We explore some general properties of minimal surfaces, and their historical origins. I am particularly interested in the Schwarz surface, which is spanned by a regular tetrahedral skew quadrilateral. We use the Weierstrass-Enneper representation formulas to derive the analytic function $R(\omega)$ …
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Minimal Surfaces in three-sphere with special spherical symmetry
… symmetry and classify the complete regular minimal surfaces in the three sphere having this symmetry. We also show that the Clifford torus is the unique embedded minimal torus in three sphere possessing special spherical symmetry.
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A New Approach to Lie Symmetry Groups of Minimal Surfaces
<p>The Lie symmetry groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the …
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On Connections Between Univalent Harmonic Functions, Symmetry Groups, and Minimal Surfaces
… of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the Weierstrauss-Enneper representation formula. …
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The Numerical approximation of minimal surfaces with free boundaries by finite elements
… discrete approximations to following disc-type minimal surfaces with free boundaries: Solution of the Plateau Problem corresponding to a supporting surface S, Solution of the Thread Problem. In both case, the problem is reformulated and the highly nonlinear problem (obtained) is discretized …
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Norms on cohomology, harmonic forms, eigenvalues and minimal surfaces in hyperbolic manifolds
… and cusped cases, using the interaction of minimal surfaces and harmonic forms. We unify various results by defining two functionals on orientable closed and cusped hyperbolic-manifolds, and formulate several questions and conjectures. Using similar decomposition principles, we also obtain …
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From Pine Cones to Minimal Surfaces: The Geometry and Mechanics of Morphing Bilayers
… de-localisation of the boundary layer, noting a minimal surface for opposite-sense prestressing for two-dimensional de-localisation. This dissertation thus provides an insight into the role edge effects play on bilayers in the context of disparate planform geometries, which we further combine …
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Conformal and asymptotic properties of embedded genus-g minimal surfaces with one end
… in their study of the structure of embedded minimal surfaces in R3 [12, 19-22], we investigate the conformal and asymptotic properties of complete, embedded minimal surfaces of finite genus and one end. We first present a more geometric proof of the uniqueness of the helicoid than the …
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On two-valued minimal graphs and minimal surfaces arising from the Allen-Cahn equation
… parts. The first discusses so-called two-valued minimals, and takes up the majority of the text. It concludes with a proof of a Bernstein-type theorem valid in dimension four: in this dimension entire two-valued minimal graphs are linear. In gross terms we follow a strategy similar to that used …
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Triply Periodic Minimal Surfaces as structured porous media cooling systems for the removal of high heat fluxes
L'abstract è presente nell'allegato / the abstract is in the attachment
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A Mathematical Development of Minimal Surface Theory: From Soap Films to Black Holes
<p>Minimal surfaces are a special subset of surfaces that have gone through a long and extensive development and have also led to many fruitful findings in mathematics. Several periods that are key to the progression of the theory are coined as Golden Ages for the field’s development. Here, a …
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Mean curvature flow self-shrinkers with genus and asymptotically conical ends
This doctoral dissertation is on the theory of Minimal Surfaces and of singularities in Mean Curvature Flow, for smooth submanifolds Y" in an ambient Riemannian (n+ 1)-manifold Nn+1, including: (1) New asymptotically conical self-shrinkers with a symmetry, in R"+1. (1') Classification of complete …
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On special Kähler metrics and hypersurfaces
Minimal surfaces in 3-manifolds play an important role in 3-dimensional geometry. In higher dimensions, there are special geometric structures, including Ricci-flat Kähler structures on complex manifolds. They are called Calabi-Yau manifolds. Generalizations include Kähler-Ricci soliton structures. …
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Equivariant Deformations of Horospherical Surfaces
The classical Goursat transform for minimal surfaces is interpreted as conformal transformation of the Gauss map, allowing us to "bend" these surfaces for certain geometric purposes. A simple analogue of this deformation is defined for CMC1 surfaces which makes the Goursat transform equivariant …
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Aspects of the reflected entropy
… inside the entanglement wedge, called reflected minimal surfaces. From the bulk point of view, we show that half the area of the reflected minimal surface, in Planck units, gives a reinterpretation of the notion of the entanglement wedge cross-section. In doing so, we address the connection with …
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Solitons and Volume Preserving Flow
… preserving flow will be used to investigate minimal surfaces in the context of double bubbles. Work will reproduce explicit results for double bubbles on the two-torus and construct a range of possible minimisers on the three-torus. Domain walls in a Wess-Zumino model with a triply degenerate …
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Existence and regularity of monotone solutions to a free boundary problem
… the 8-dimensional Simons cone in the theory of minimal surfaces. The minimality of the Simons cone is closely related to the existence of a complete minimal graph in dimension 9, which is not a hyperplane. The first step toward solving the analogous problem in the free boundary context, consists …
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Topics in geometric analysis with applications to partial differential equations
… geometry is variable, such as: -- the theory of minimal surfaces, in differential geometry -- shape analysis and optimization-- engineering modeling -- (elasticity phenomena for beams, plates, shells, etc) -- free or moving boundary problems -- certain variational problems in partial differential …
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