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The Schwarz lemma for nonpositively curved Riemannian surfaces

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MAP-Based Error Correction Mechanism for Five-Key Chording Keyboards

Pierre Dillenbourg, Bixio Rimoldi, Adrian Dan Tarniceriu

Because of different designs, different text input devices have different error patterns. If we consider these aspects when designing an error correction mechanism, we can obtain significantly lower error rates. In this paper, we propose and evaluate a spe ...

2015

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Martins Bruveris, Martin Bauer

This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics th ...

Springer Verlag2014

The impossible here

André Ourednik

The recurring challenge facing anyone who tries to localize realities in order to show their spatial relations on a map is the systematic impermanence of any objectivized space. Thus any space used as a base layer in thematic maps must be thought of as the ...

2014

An improvement on geometrical parameterizations by transfinite maps

Gianluigi Rozza, Laura Iapichino, Christoph Jäggli

We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon–Hall transfinite interpolation approach. It is defined globally over the reference domain. ...

Elsevier France-Editions Scientifiques Medicales Elsevier2014

Low-Rank Matrix Completion By Riemannian Optimization

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over the Riemannian ma ...

Siam Publications2013

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

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martins Bruveris, Martin Bauer

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 ...

Springer Verlag2013

Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra

Zahra Sinaei

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 ...

EPFL2013

Closing Large Hyperbolic 2g-gons

Poincaré's uniformisation theorem says that any Riemann surface is conformally equivalent to a unique (up to isometry) surface of constant Gauss curvature 0, 1 or –1. The (topologically) richest of these three worlds is for curvature –1 formed of hyperboli ...

EPFL2012

Scalar geometry and masses in Calabi-Yau string models

Claudio Scrucca, Daniel Farquet

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 ...

Springer2012