Concept

Curvature of Riemannian manifolds

Related publications (167)

Optimal control of geodesics in Riemannian manifolds

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

A heuristic for global nonlinear optimization

Michel Bierlaire, Michaël Clément Louis Ghislain Thémans, Nicolas Zufferey

The proposed heuristic combines a variable neighborhood search (VNS) framework with a local search performed by a trust-region algorithm. The curvature of the function is exploited to generate the neighborhoods. Numerical results illustrate an excellent be ...

2007

Metastable supergravity vacua with F and D supersymmetry breaking

Claudio Scrucca

We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit viable metastable vacua with spontaneously broken supersymmetry and realistic cosmological constant. To do so, we impose that on the vacuum th ...

2007

Image alignment with rotation manifolds built on sparse geometric expansions

Pascal Frossard, Effrosyni Kokiopoulou

In this paper we discuss the problem of alignment of patterns under arbitrary rotation. When a generic image pattern is geometrically transformed, it typically spans a (possibly nonlinear) manifold in a high dimensional space. When the pattern of interest ...

2007

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Marc Troyanov

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold

(M,g)

and the

L_{q,p}

-cohomology of that manifold. The

L_{q,p}

-cohomology of

(M,g)

is defined to be the quotient of the space of closed differential ...

2006

Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position

Christian Depeursinge, Tristan Colomb, Etienne Cuche, Frédéric Montfort, Pierre Marquet, Florian Charrière

Introducing a microscope objective in an interferometric setup induces a phase curvature on the resulting wavefront. In digital holography, the compensation of this curvature is often done by introducing an identical curvature in the reference arm and the ...

2006

Wavelets on non-Euclidean manifolds

Iva Bogdanova Vandergheynst

This dissertation investigates wavelets as a multiscale tool on non-Euclidean manifolds. The growing importance of using non-Euclidean manifolds as a geometric model for data comes from the diversity of the data collected. In this work we mostly deal with ...

EPFL2006

Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Iva Bogdanova Vandergheynst

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This tech ...

2005

Optimal control of geodesics in Riemannian manifolds

Klaus-Dieter Semmler, Roland Rozsnyo

Summary: We present a method based on an optimal control technique for numerical computations of geodesic paths between two fixed points of a Riemannian manifold under the assumption of existence. In this method, the control variable is the tangent vector ...

2004

Development of Insulated Conductive Probes with Platinum Silicide Tips for Atomic Force Microscopy in Cell Biology

Nico de Rooij, Terunobu Akiyama

A microfabrication process of a multifunctional probe is introduced for atomic force microscopy and various electrochemical measurements on biological samples in buffer solution. The silicon nitride probes have a spring constant lower than 0.1 N/m and a co ...

2004

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Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Iva Bogdanova Vandergheynst

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This tech ...

2005

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Marc Troyanov

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold

(M,g)

and the

L_{q,p}

-cohomology of that manifold. The

L_{q,p}

-cohomology of

(M,g)

is defined to be the quotient of the space of closed differential ...

2006