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 44 for “"riemannian manifold"”.
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Brownian motions on a Riemannian manifold
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1961.
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On the conjugate locus of a Riemannian manifold.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1966
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Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
… study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion …
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Path optimization using sub-Riemannian manifolds with applications to astrodynamics
… path optimization problems will generate a sub-Riemannian manifold. This work describes an algorithm which approximates a sub-Riemannian manifold as a Riemannian manifold using a penalty metric so that Riemannian geodesic solvers can be used to find the solutions to the path optimization …
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Scalar curvature on noncompact complete Riemannian manifolds
Let (M,g) be a noncompact complete Riemannian manifold whose scalar curvature S(x) is positive for all x in M. In this thesis, we study a conformal deformation of the given metric g, which makes the scalar curvature of the deformed metric a positive constant. We also study the existence of a …
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Quantitative Topology of Loop Space
… in the based loop space of a simply connected Riemannian manifold controls its topology. Analogous to Gromov’s notion of distortion of higher homotopy groups of underlying Riemannian manifold, we define notions of distortion for (co)homology classes in the loop space with real coefficients, and …
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Geometric and dynamical properties of Riemannian foliations
Given a Riemannian foliation ${\cal F}$ on a Riemannian manifold M with a bundle-like metric, geometric and dynamical properties of geodesics orthogonal to the leaves of the foliation are studied.
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Open strings in the cotangent bundle and Morse homotopy
Let M be a riemannian manifold of dimension 3. We study the genus zero open rigid J-holomorphic curves in T*M with boundaries mapped in perturbations of the zero section. The perturbations of the zero section is defined fixing a. set of functions on M. We consider the graphs of the differential of …
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Riemannian Metric Learning via Optimal Transport
… of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field and efficiently optimize our model's objective using backpropagation. Using this learned metric, we can nonlinearly interpolate between probability measures …
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Geometric quantization and dynamical constructions on the space of Kähler metrics
… a fixed cohomology class on a compact Kähler manifold. The first part of the Thesis is concerned with a problem of geometric quantization: Can the geometry of the infinite-dimensional space of Kähler metrics be approximated in terms of the geometry of the finite-dimensional spaces of …
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ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ
… IS TO EXAMINE THE CLOSED GEODESICS ON COMPACT RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE; THAT MEANS RIEMANNIAN MANIFOLDS WHICH CAN CARRY A RIEMANNIAN METRIC WITH STRICTLY NEGATIVE SECTIONAL CURVATURE. IT ISPROVED, THAT THE INDEX OF THE M- COVER OF ONE CLOSED GEODESIC ON A COMPACT RIEMANNIAN, …
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Riemannian geometry for inverse problems in cryogenic electron microscopy
This thesis develops theory and algorithms for a Riemannian geometric approach to inverse problems in cryogenic electron microscopy (Cryo-EM). It is divided into two parts, motivated by the sub problem of orientation estimation and that of modelling of protein dynamics. The thesis is concluded with …
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Perturbation theory for the topological pressure in analytic dynamical systems
… for an analytic expanding dynamics (/, M) on a Riemannian manifold M. The method is based on the spectral analysis of the transfer operator C. We show that in typical cases, when / depends real-analytically on a set of perturbing parameters ,", the related operators C~ form an analytic family. …
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Recovering a Riemannian Metric from Knowledge of the Areas of Properly-Embedded, Area-Minimizing Surfaces
… that if (M,g) is a C3-smooth, 3-dimensional Riemannian manifold with mean convex boundary ∂M, which is additionally either a) C2-close to Euclidean or b) sufficiently thin, then knowledge of the least areas circumscribed by any simple closed curve γ ⊂ ∂M uniquely determines the metric. In …
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A tensor product approach to non-local differential complexes
… a Poincaré lemma, and show that, in the compact Riemannian manifold case, the de Rham cohomology is recovered.
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Path integrals on manifolds with boundary and their asymptotic expansions
… that solutions to the heat equation on a Riemannian manifold can be represented by a path integral. However, the problem with such path integrals is that they are notoriously ill-defined. One way to make them rigorous (which is often applied in physics) is finite-dimensional approximation, …
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On two problems related to the Laplace operator
… set of compact domains of fixed volume v in any Riemannian manifold (M; g) and where ε(Ω) is the mean exit time from of the Brownian motion. Concerning this functional, we study its critical points and prove that they are harmonic domains. We analyze the special case of the Coarea formula when we …
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Efficient Sampling Methods of, by, and for Stochastic Dynamical Systems
… and show that it accelerates convergence of Riemannian manifold Langevin dynamics more than standard irreversible perturbations. We then propose the transport map unadjusted Langevin algorithm (TMULA), and show that the use of transport enables rapid convergence of the unadjusted Langevin …
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A Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds
… we study the conjecture by embedding graphs into Riemannian manifolds using a geometric framework developed by Xiahou el al. [32]. We prove that isometric embedding of graphs into a Riemannian manifold is impossible. Then, interestingly, we construct an embedding that achieves an infinitesimally …
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A characterization of Bi-Lipschitz embeddable metric spaces in terms of local Bi-Lipschitz embeddability
… Hence we obtain the first example of a sub-Riemannian manifold admitting such a bi-Lipschitz embedding. Our techniques involve a passage from local to global information, building on work of Christ and McShane. A new feature of our proof is the verification of the co-Lipschitz condition. …
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