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 16 of 16 for “"Metric geometry"”.
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Quasi-metric geometry
… one sees |x-y|, one is looking at a specific metric acting on x and y, whatever they may happen to be, usually numbers or vectors. The notion of the distance between two objects is one of the most fundamental and ubiquitous in many branches of mathematics. A quasi-metric is a generalization of …
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Combinatorics and Metric Geometry
This thesis consists of an introduction and seven chapters, each devoted to a different combinatorial problem. In Chapters 1 and 2, we consider the main subject of this thesis; the sharp stability of the Brunn-Minkowski inequality (BM). This celebrated theorem from the 19th century asserts that for …
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Metric Geometry of Finite Subset Spaces
… any subclass C of homeomorphisms in H(X), the C-geometry of X refers to the description of X up to homeomorphisms in C. Therefore, the topology of X is the H(X)-geometry of X. By a (C-) geometric property of X we will mean a property of X that is preserved by homeomorphisms of X (in C). Metric …
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Metric geometry of the Grushin plane and generalizations
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms
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Metric Geometry of Quiver Flag Varieties and Balanced Embeddings
… multiple of the identity matrix. A hermitian metric on a line bundle is balanced if its Bergman kernel is identically constant. We study the relationship between balanced manifolds and balanced metrics, and generalize their correspondence to the case of weakly exceptional sequence of globally …
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Theory and applications of a functional from metric geometry
… energy integral $J\sp\alpha$ has its roots in metric embedding theory and potential theory. Subject to certain moment vanishing conditions, a representation formula is proved using the Fourier transform and tempered distributions. Ideas from integral geometry are used to apply the functional …
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Topics in metric geometry, combinatorial geometry, extremal combinatorics and additive combinatorics
… in the thesis title. Given a non-empty complete metric space $(X,d)$, a family of $n$ continuous maps $f_1,f_2,\dots,f_n\colon X\to X$ is a \emph{contractive family} if there exists $\lambda<1$ such that for any $x,y\in X$ we have $d(f_i(x),f_i(y))\leq\lambda d(x,y)$ for some $i$. In the first …
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Quantitative embeddings with applications
… of these quantitative embeddings to a problem in metric geometry related to the isoperimetric inequality and a problem about constructing local quantum error-correcting codes.
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Vietoris–Rips metric thickenings and Wasserstein spaces
… vertex set, X, of a simplicial complex, K, is a metric space, then K can be interpreted as a subset of the Wasserstein space of probability measures on X. Such spaces are called simplicial metric thickenings, and a prominent example is the Vietoris–Rips metric thickening. In this work we study …
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3D reconstruction and camera calibration from 2D images
… is equivalent to the estimation of a specific geometry group. The first step is the estimation of the epipolar geometry that exists between the stereo image pair, a process involving feature matching in both images. The second step estimates the affine geometry, a process of finding a special …
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Quantum Metrics on Approximately Finite-Dimensional Algebras
… (AF) algebras into the realm of noncommutative metric geometry. We construct quantum metric structures on unital AF algebras equipped with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite dimensional C*-algebras for …
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The Fundamental Group: A Geometric Perspective
… and the rigid, distance-preserving world of metric geometry. We begin by constructing the fundamental group of a topological space, using the concept of loops and loop homotopy to identify a global topological invariant such as a hole or puncture. We then transition to the geometric realm of …
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The Effect of Computer Programming on The Problem-Solving Strategies of Preservice Teachers
… groups were made up of students enrolled in "Metric Geometry and Teaching Elementary Mathematics" and "Instructional Tasks in the Secondary School." The computer language taught to the experimental group was BASIC. A variation of the "Nonequivalent Control Group Design" as described by …
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Continuum Methods and Tightness Results for Non-Simple SLE and CLE: Existence, Interactions, and Metric Approximations
… We bypass discrete models by using the imaginary geometry framework, in which SLE curves arise as flow lines of the Gaussian Free Field (GFF). We work with whole-plane space-filling SLEκ parameterized by Lebesgue measure, and establish uniform estimates on its behavior as κ↑8. A tightness argument …
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Hitchin Functionals, h-Principles and Spectral Invariants
… then proceeds to interpret this unboundedness geometrically, demonstrating an unexpected link between the functional $\mathcal{H}_3$ and fibrations, proving that the 'large volume limit' of $\mathcal{H}_3$ in each case corresponds to the adiabatic limit of a suitable fibration. The proof utilises …