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Concept

Géodésique

Publications associées (31)

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Martins Bruveris

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

Quasiconformal Embeddings of Y-Pieces

In this paper we construct quasiconformal embeddings from Y-pieces that contain a short boundary geodesic into degenerate ones. These results are used in a companion paper to study the Jacobian tori of Riemann surfaces that contain small simple closed geod ...

Springer Heidelberg2014

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

Martins Bruveris

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

Resting-brain functional connectivity predicted by analytic measures of network communication

Jean-Philippe Thiran, Patric Hagmann, Alessandra Griffa

6 The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structur ...

National Academy of Sciences2014

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

Martins Bruveris

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) ...

Springer Verlag2013

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

Martins Bruveris

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

Computational Approach to the Geometry of Compact Riemann Surfaces

Manuel Racle

The goal of this document is to provide a generalmethod for the computational approach to the topology and geometry of compact Riemann surfaces. The approach is inspired by the paradigms of object oriented programming. Our methods allow us in particular to ...

EPFL2013

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

The degenerate two well problem for piecewise affine maps

Bernard Dacorogna

The two well problem consists in finding maps u which satisfy some boundary conditions and whose gradient Du assumes values in the two wells . Here (similarly ) is the well generated by a 2 x 2 matrix A, i.e., is the set of matrices of the form RA, where R ...

Springer Basel Ag2013

Invariant Higher-Order Variational Problems II

Tudor Ratiu, François Gay-Balmaz

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as ...

Springer Verlag2012

Publications associées (31)