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We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...
The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...
The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an L-q,L-p-Sobolev inequality (2
A multimodal haptic device operating as a closed-loop system, the device including a pipeline configured to allow a closed-loop flow of a fluid medium, a manifold operatively connected to the pipeline, the manifold having a pump and a valve to control and ...
We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds X of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are d-fold products of 2-spheres or 3-spheres, realiz ...
We propose a segmentation method based on the geometric representation of images as two-dimensional manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set ...
Institute of Electrical and Electronics Engineers2014
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...
We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...
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 ...