Publications associées à Hermann Minkowski

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

We consider the hyperbolic Yang-Mills equation on the Minkowski space

\reels^{4+1}

. Our main result asserts that this problem is globally well-posed for all initial data whose energy is sufficiently small. This solves a longstanding open problem. ...

Annal Mathematics2017

Minkowski space is locally the Noldus limit of Poisson process causets

Jan Cristina

A Poisson process P-lambda on R-d with causal structure inherited from the the usual Minkowski metric on R-d has a normalised discrete causal distance D-lambda (x, y) given by the height of the longest causal chain normalised by lambda(1/d)c(d). We prove t ...

Iop Publishing Ltd2016

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation

Joachim Krieger

We prove global regularity, scattering and a priori bounds for the energy critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge on (1+4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gerard profile decomposition [1] ...

2015

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Joachim Krieger, Roland Donninger, Willie Wai Yeung Wong

We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy pro ...

Duke Univ Press2015

Planck 2013 results. XXV. Searches for cosmic strings and other topological defects

Julien Lesgourgues, Jason Douglas McEwen, Fabio Finelli

Planck data have been used to provide stringent new constraints on cosmic strings and other defects. We describe forecasts of the CMB power spectrum induced by cosmic strings, calculating these from network models and simulations using line-of-sight Boltzm ...

Edp Sciences S A2014

On stability of the catenoid under vanishing mean curvature flow on Minkowski space

Joachim Krieger

We establish basic local existence as well as a stability result concerning small perturbations of the Catenoid minimal surface in R-3 under hyperbolic vanishing mean curvature flow. ...

International Press2012

On stable self-similar blow up for equivariant wave maps: The linearized problem

Roland Donninger

We consider co-rotational wave maps from (3+1) Minkowski space into the three-sphere. This is an energy supercritical model which is known to exhibit finite time blow up via self-similar solutions. The ground state self-similar solution

f_0

is known in c ...

2012

Concentration Compactness for critical wave maps

Joachim Krieger

Wave maps are the simplest wave equations taking their values in a Riemannian manifold (M,g). Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric g. By Noether's theorem, s ...

European Mathematical Society2012

Hermann Minkowski

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Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

Minkowski space is locally the Noldus limit of Poisson process causets

Inhomogeneous minima of mixed signature lattices

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Planck 2013 results. XXV. Searches for cosmic strings and other topological defects

On stability of the catenoid under vanishing mean curvature flow on Minkowski space

On stable self-similar blow up for equivariant wave maps: The linearized problem

Concentration Compactness for critical wave maps

On stable self-similar blow up for equivariant wave maps: The linearized problem

Minkowski space is locally the Noldus limit of Poisson process causets

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Planck 2013 results. XXV. Searches for cosmic strings and other topological defects

Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation

Inhomogeneous minima of mixed signature lattices

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

On stability of the catenoid under vanishing mean curvature flow on Minkowski space

Concentration Compactness for critical wave maps