Publications related to Infinite dimensional geodesic flows and the universal Teichmüller space

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The geometry of the universal Teichmuller space and the Euler-Weil-Petersson equation

Tudor Ratiu, François Gay-Balmaz

On the identity component of the universal Teichmuller space endowed with the Takhtajan-Teo topology, the geodesics of the Weil Petersson metric are shown to exist for all time. This component is naturally a subgroup of the quasisymmetric homeomorphisms of ...

Elsevier2015

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ_1

Nisheeth Vishnoi

In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative type metric embeds into ℓ1 with constant distortion. We show that for an arbitrarily small constant δ > 0, for all large enough n, there is an n-point negative ...

Association for Computing Machinery2015

A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries

Assyr Abdulle, Ondrej Budác

We present a Petrov-Galerkin reduced basis (RB) approximation for the parameterized Stokes equation. Our method, which relies on a reduced solution space and a parameter-dependent test space, is shown to be stable (in the sense of Babuska) and algebraicall ...

Elsevier2015

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Martins Bruveris, Martin Bauer

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...

Springer Verlag2014

Harmonic Active Contours

Jean-Philippe Thiran, Xavier Bresson, Dominique Zosso, Virginia Estellers Casas

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

Principal Polynomial Analysis

Devis Tuia

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...

World Scientific Publ Co Pte Ltd2014

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

Infinite dimensional geodesic flows and the universal Teichmüller space

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The geometry of the universal Teichmuller space and the Euler-Weil-Petersson equation

The Fluid Joint: The Soft Spot of Micro- and Nanosystems

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ_1

A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

The connectivity at infinity of a manifold and Sobolev inequalities

Harmonic Active Contours

Principal Flows

Principal Polynomial Analysis

Total Variation Regularization for Manifold-Valued Data

A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries

Principal Polynomial Analysis

The geometry of the universal Teichmuller space and the Euler-Weil-Petersson equation

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ_1

The connectivity at infinity of a manifold and Sobolev inequalities

Harmonic Active Contours

The Fluid Joint: The Soft Spot of Micro- and Nanosystems

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Principal Flows

Total Variation Regularization for Manifold-Valued Data