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Solving the $p$-Laplacian on manifolds

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L-2-cohomology and complete Hamiltonian manifolds

Tudor Ratiu

A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem st ...

Elsevier2015

The connectivity at infinity of a manifold and Sobolev inequalities

Marc Troyanov

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

Elsevier2014

, , ,

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

Principal Flows

Victor Panaretos, Tung Huy Pham, Zhigang Yao

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 ...

American Statistical Association2014

Total Variation Regularization for Manifold-Valued Data

Martin Kurt Storath

We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(p) -type data terms in the manifold case. These algorithms are ba ...

Siam Publications2014

An Exotic Deformation of the Hyperbolic Space

Nicolas Monod

Let Isom(H^n) be the group of isometries of the n-dimensional real hyperbolic space. We first classify all continuous non-elementary actions of on the infinite-dimensional real hyperbolic space. We then prove the existence of a continuous family of non-iso ...

Johns Hopkins Univ Press2014

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 ...

Cambridge Univ Press2013

Learning Smooth Pattern Transformation Manifolds

Pascal Frossard, Elif Vural

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that are ob ...

Institute of Electrical and Electronics Engineers2013

Tangent space estimation for smooth embeddings of Riemannian manifolds

Pascal Frossard, Elif Vural, Hemant Tyagi

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 ...

2013

Learning Pattern Transformation Manifolds for Classification

Pascal Frossard, Elif Vural

Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection ...

2012