Publications related to A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

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

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

Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity

Claudio Scrucca

We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral super fields. Starting from the two necessary conditions for fl ...

2006

Piecewise flat Metrics on Surfaces and the Moduli Space

Marc Troyanov

We show how the theory of deformations of geometric structures (development and holonomy) applied to the case of piecewise flat surfaces leads to some interesting geometric structures on the moduli space of a punctured surface. ...

2006

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

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

Liouville type theorems for mappings with bounded (co)-distortion

Marc Troyanov

We obtain Liouville type theorems for mappings with bounded

s

-distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded

q

-codistorsion. ...

2002

Boundary behavior of quasi-regular maps and the isodiametric profile

Marc Troyanov

We study obstructions for a quasi-regular mapping f : M -> N of finite degree between Riemannian manifolds to blow up on or collapse on a non-trivial part of the boundary of M. ...

2001

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

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

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

Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity

Piecewise flat Metrics on Surfaces and the Moduli Space

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

Optimal control of geodesics in Riemannian manifolds

Stereographic Frames of Wavelets on the Sphere

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

Liouville type theorems for mappings with bounded (co)-distortion

Boundary behavior of quasi-regular maps and the isodiametric profile

Replacement manifolds: A method to uniformize semiclassical wave functions

Boundary behavior of quasi-regular maps and the isodiametric profile

Replacement manifolds: A method to uniformize semiclassical wave functions

Optimal control of geodesics in Riemannian manifolds

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

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

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

Piecewise flat Metrics on Surfaces and the Moduli Space

Liouville type theorems for mappings with bounded (co)-distortion

Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity

Stereographic Frames of Wavelets on the Sphere