Publications related to Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Weak Finsler structures and the Funk weak metric

We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distance ...

Cambridge University Press2009

Differential geometry: a natural tool for describing symmetry operations

Gervais Chapuis, Kurt Schenk, Philippe Kocian

Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group o ...

2009

Minimum distance between pattern transformation manifolds: Algorithm and Applications

Pascal Frossard, Effrosyni Kokiopoulou

Transformation invariance is an important property in pattern recognition, where different observations of the same object typically receive the same label. This paper focuses on a transformation invariant distance measure that represents the minimum dista ...

2009

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Bernard Dacorogna

Any finite, separately convex, positively homogeneous function on

\mathbb{R}^2

is convex. This was first established by the first author ["Direct methods in calculus of variations", Springer-Verlag (1989)]. Here we give a new and concise proof of this re ...

2008

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Madeleine Jotz

In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence ...

2008

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Alireza Karimi, Roland Longchamp, Hamid Khatibi

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex inner-approximation of the whole non- convex set of stabilizing control ...

2008

Optimal control of geodesics in Riemannian manifolds

Roland Rozsnyo

The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...

EPFL2007

Inclusions différentielles et problèmes variationnels

Ana Margarida Fernandes Ribeiro

In this thesis we deal with three different but connected questions. Firstly (cf. Chapter 2) we make a systematic study of the generalized notions of convexity for sets. We study the notions of polyconvex, quasiconvex and rank one convex set. We remark tha ...

EPFL2006

Perfect Simulation and Stationarity of a Class of Mobility Models

Jean-Yves Le Boudec, Milan Vojnovic

We define ``random trip", a generic mobility model for independent mobiles that contains as special cases: the random waypoint on convex or non convex domains, random walk with reflection or wrapping, city section, space graph and other models. We use Palm ...

2005

Thurston's weak metric on the Teichmüller space of the torus

Marc Troyanov

We define and study a natural weak metric on the Teichmüller space of the torus. A similar metric has been defined by W. Thurston on the Teichmüller space of higher genus surfaces and our definition is motivated by Thurston's definition. However, we shall ...

2005

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

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Weak Finsler structures and the Funk weak metric

Differential geometry: a natural tool for describing symmetry operations

Minimum distance between pattern transformation manifolds: Algorithm and Applications

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Optimal control of geodesics in Riemannian manifolds

Inclusions différentielles et problèmes variationnels

Perfect Simulation and Stationarity of a Class of Mobility Models

Thurston's weak metric on the Teichmüller space of the torus

Optimal control of geodesics in Riemannian manifolds

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Inclusions différentielles et problèmes variationnels

Weak Finsler structures and the Funk weak metric

Differential geometry: a natural tool for describing symmetry operations

Perfect Simulation and Stationarity of a Class of Mobility Models

Minimum distance between pattern transformation manifolds: Algorithm and Applications

Thurston's weak metric on the Teichmüller space of the torus