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 13 of 13 for “"geometric measure theory"”.
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Distance Sets and Gap Lemma
Many problems in geometric measure theory are centered around finding conditions and structures on a set to guarantee that its distance set must be large. Two notions of structure that are of importance in this work are Hausdorff dimension and thickness. Recent progress has been made on …
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Detection of non-coding RNA with comparative genomics and the sequential closure of smooth graphs in Cartesian currents
… scanning cDNA for ncRNA genes. In the field of geometric measure theory, it proves that the set of cartesian currents given by integration over the graphs of smooth functions is dense in the set of all cartesian currents.
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Local Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applications
In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space through studying a class of sets S which approximates A well in small balls. We …
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The Mattila-Sjölin Problem for Triangles
… problem which establishes a positive Lebesgue measure for the distance set instead of it having nonempty interior
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A Novel Image Retrieval Strategy Based on VPD and Depth with Pre-Processing
… can be merged into the original model based on geometric measure theory. Experiments illustrate this model is effective for image denoising, and it can improve the retrieval performance by denoising a query image. A model is proposed for image restoration. It is an extension of the traditional …
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A Mass Minimizing Flow for Real-Valued Flat Chains with Applications to Transport Networks
An oriented transportation network can be modeled by a 1-dimensional chain whose boundary is the difference between the demand and supply distributions, represented by weighted sums of point masses. To accommodate efficiencies of scale into the model, one uses a suitable Mα norm for transportation …
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Local Criteria in Polyhedral Minimizing Problems
This thesis will discuss two polyhedral minimizing problems and the necessary local criteria we find any such minimizers must have. We will also briefly discuss an extension of a third minimizing problem to higher dimension. The first result we present classifies the three-dimensional piecewise …
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Hausdorff Dimension of Wildly Embedded Zero Dimensional Subspaces of R³
No abstract prepared.
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On the Variational Theory of Yang-Mills-Higgs Energies and the Structure of the Singular Set of $\mathbb{Z}$$_{2}$-Harmonic Spinors
… Pigati and Daniel Stern on the variational theory of the self-dual U(1)-Yang-Mills-Higgs functionals on a closed Riemannian manifold (M,g). This natural family of energies associated with sections u: M → L and metric connections ∇ of Hermitian line bundles has long been studied in …
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Structure of Singular Sets Local to Cylindrical Singularities for Stationary Harmonic Maps and Mean Curvature Flows
In this paper we prove structure 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. …
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On the Structure and Regularity of Stable Branched Minimal Hypersurfaces
… the 1970's from the De Giorgi--Allard regularity theory ([All72]) and the structure theory of White ([Whi79]) respectively. The implication to mod $p$ minimising currents of the structure theory for $\mathcal{S}_{p/2}$ is analogous to how the regularity theory for codimension one integral currents …
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Estimating the Intrinsic Dimension of High-Dimensional Data Sets: A Multiscale, Geometric Approach
<p>This work deals with the problem of estimating the intrinsic dimension of noisy, high-dimensional point clouds. A general class of sets which are locally well-approximated by <italic>k</italic> dimensional planes but which are embedded in a <italic>D</italic>>><italic>k</italic> dimensional …
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On two-valued minimal graphs and minimal surfaces arising from the Allen-Cahn equation
… which echo those available in the classical theory. The main contrast with these historical results is the possible presence of a large set of singularities. This is exacerbated by the fact that two-valued minimal graphs do not minimise area, unlike their single-valued counterparts. As a …