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Showing 1 to 7 of 7 for “"Morse function"”.
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Dynamic Modeling With Implicit Surfaces and Polygonal Meshes
"Morse theory reveals the topological structure of a shape based on the critical points of a real function over the shape. This thesis solves a relaxed form of Laplace's equation to find a ""fair"" Morse function with a user-controlled number and configuration of critical points."
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Special gradient trajectories counted by simplex straightening
… on a manifold with boundary. And third, the Morse broken trajectory theorem relates the simplicial volume to the number of maximally broken trajectories of the gradient flow of a Morse--Smale function. Corollary: a Morse function on a closed hyperbolic manifold must have a critical point of …
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On two problems related to the Laplace operator
We investigate maximization of the functional Ω → ε(Ω) where Ω runs in the 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 …
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Moduli spaces and cw structures arising from morse theory
… the moduli spaces and CW Structures arising from Morse theory.</p> <p>Suppose M is a smooth manifold and f is a Morse function on it. We consider the negative gradient flow of f. Suppose the flow satisfies transversality. This naturally defines the moduli spaces of flow lines and gives a …
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Shape Modeling and Analysis for Object Representation, Reconstruction, and Recognition
… 2D and 3D shape models are formulated in a Morse theoretic framework, where shapes of arbitrary topology are represented completely by topo-geometric graphs. The idea is to capture topology by localizing critical points of distance function as the Morse function, thereby representing it …
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Topological Approaches to Chromatic Number and Box Complex Analysis of Partition Graphs
… techniques. Lastly, we apply discrete Morse theory to construct a simplicial complex homotopy equivalent to the box complex of P(33), using two methods: elementary collapses and the determination of a discrete Morse function on the box complex. This process reduces the dimension of the …