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Showing 1 to 20 of 52 for “"Riemannian manifolds"”.
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Slice sampling on Riemannian manifolds
… for approximate sampling of distributions on Riemannian manifolds. First for distributions on the Euclidean unit sphere, and then for distributions on general Riemannian manifolds we introduce a geodesic-based hybrid slice sampler, called geodesic slice sampler. Under mild regularity …
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Decomposition Theorems of Riemannian Manifolds
Made available in DSpace on 2014-12-11T18:24:05Z (GMT). No. of bitstreams: 1 7405729.pdf: 1917028 bytes, checksum: fad596ca7cba5104585fe542ba8a5bfc (MD5) Previous issue date: 1973
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Conformal Vector Fields on Compact Riemannian Manifolds
Made available in DSpace on 2014-12-09T22:17:45Z (GMT). No. of bitstreams: 1 6812219.pdf: 1974392 bytes, checksum: 5c72a2f611b65dea6a2dacf605a251d9 (MD5) Previous issue date: 1968
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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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Parallelism on p-surfaces in Riemannian manifolds.
Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1965. Ph.D.
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Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks
The combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications. However, both literatures contain fundamental unsolved problems. The thesis is thus in two main parts. In part I, we …
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Sobolev tests for uniformity on compact Riemannian manifolds,
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1973
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From Proximal Point Method to Accelerated Methods on Riemannian Manifolds
… successful ideas in Euclidean optimization to Riemannian optimization. However, one landmark result of Euclidean optimization has eluded the Riemannian setting: namely, a Riemannian analog of Nesterov's accelerated gradient method (AGM). In this thesis, we establish the first globally …
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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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Kähler structures on cotangent bundles of real analytic Riemannian manifolds
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1990.
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On-diagonal heat kernel bounds and volume growth on Riemannian manifolds
… positive reals and $c_{x}$ may depend on $x$, on manifolds having at least one end with a polynomial volume growth.
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Strichartz estimates for the wave equation on Riemannian manifolds of bounded curvature
… methods to prove Strichartz estimates on compact Riemannian manifolds under the condition that the Riemannian curvature tensor is uniformly bounded. This improves upon prior results for the case of metrics with two bounded derivatives.
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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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Geometric mapping theory of the Heisenberg group, sub-Riemannian manifolds, and hyperbolic spaces
… model (metric tangent space) of some sub-Riemannian manifolds and allows one to study derivatives of mappings between such spaces. As a subgroup of the isometry group of complex hyperbolic space $\Hyp^{n+1}_\C$, $\Heis^n$ becomes a large-scale model of a rank-one symmetric space and …
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Well-Posedness Threshold and Moment Asymptotics of the Parabolic Anderson Model on Riemannian Manifolds
… heat equation. We consider the equation on Riemannian manifolds to study how geometry and topology can affect interesting properties of the solution. We focus on two topics: well-posedness and large time moment asymptotics. We first introduce the equation, the basic theory of Gaussian noises …
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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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Tracking on manifolds : quasi-Newton optimisation algorithms on manifolds
In recent years, optimisation on manifolds has become a popular area of research. Applications in signal processing have been proposed as well. Optimisation methods on manifolds can reduce the dimension of the original problems compared to the problems in their ambient Euclidean space. Many …
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Rigid Body Constrained Motion Optimization and Control on Lie Groups and Their Tangent Bundles
… utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. …
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NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS
We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure.
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