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Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Publications associées (61)

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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

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

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

Stereographic Frames of Wavelets on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this technical report the Discrete Wavelet Frames are build on the already existing Spherical Continuous Wavelet Transform. The spherical half-continuous frames are explored, i.e when the position on the sphere is kept continuous variable. Then, the con ...

2004

Global regularity of wave maps from $R^{3+1}$ to surfaces

Joachim Krieger

We consider Wave Maps with smooth compactly supported initial data of small (H) over dot (3/2)-norm from R3+1 to certain 2-dimensional Riemannian manifolds and show that they stay smooth globally in time. Our methods are based on the introduction of a glob ...

Springer Verlag2003

Replacement manifolds: A method to uniformize semiclassical wave functions

Jiri Vanicek

We present a semiclassical technique that relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor o ...

2001

Solving the p-Laplacian on manifolds

Marc Troyanov

We prove in this paper that the equation

Delta _{p}u+h=0

on a p-hyperbolic manifold M has a solution with p-integrable gradient for any bounded measurable function h : M -> R with compact support. ...

2000

Solving the $p$-Laplacian on manifolds

Marc Troyanov

We prove in this paper that the equation

\Delta _{p}u+h=0

on a

p

- hyperbolic manifold

M

has a solution with

p

-integrable gradient for any bounded measurable function

h : M \to \mathbb R

with compact support. ...

2000

Parabolicity of manifolds

Marc Troyanov

This Paper is an introduction to the study of an invariant of Riemannian manifolds related to the non-linear potential theory of the p-Laplacian and which is called its parabolic or hyperbolic type. One of our main focus is the relationship between the asy ...

1999