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Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a ...
We present results from an experimental investigation of the indentation of nonspherical pressurized elastic shells with a positive Gauss curvature. A predictive framework is proposed that rationalizes the dependence of the local rigidity of an indented sh ...
This thesis is a study of harmonic maps in two different settings. The first part is concerned with harmonic maps from smooth metric measure spaces to Riemannian manifolds. The second part is study of harmonic maps from Riemannian polyhedra to non-positive ...
We study the geometry of the scalar manifolds emerging in the no-scale sector of Kahler moduli and matter fields in generic Calabi-Yau string compactifications, and describe its implications on scalar masses. We consider both heterotic and orientifold mode ...
We prove the following version of Poincaré, duality for reduced L (q,p) -cohomology: For any 1 < q, p < a, the Lqp -cohomology of a Riemannian manifold is in duality with the interior Lp'q'-cohomology for 1/p + 1/p' = 1/q + 1/q' = 1. ...
We study Sobolev-type metrics of fractional order s a parts per thousand yen 0 on the group Diff (c) (M) of compactly supported diffeomorphisms of a manifold M. We show that for the important special case M = S (1), the geodesic distance on Diff (c) (S (1) ...
Wave maps are the simplest wave equations taking their values in a Riemannian manifold (M,g). Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric g. By Noether's theorem, s ...
The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...
We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mi ...
Insight is provided in hydrodynamic processes governing the velocity redistribution in sharp river bends based on simulations of three recent experiments by means of Blanckaert and de Vriend's (2003, 2010) reduced-order nonlinear model without curvature re ...
