Related papers: A Gaussian refinement of the Lieb-Robinson bound
We obtain new topological information about the local structure of collapsing under a lower sectional curvature bound. As an application we prove a new sphere theorem and obtain a partial result towards the conjecture that not every…
This paper has been withdrawn by the authors in order to replace it with a more correct treatment. The basic results remain the same but the treatment is more rigorously correct.
This paper has been withdrawn because of serious errors.
This paper has been withdrawn due to a crucial theoretical and experimental error.
A lower bound for the Gaussian Q-function is presented in the form of a single exponential function with parametric order and weight. We prove the lower bound by introducing two functions, one related to the Q-function and the other…
We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi's counterexample. Here we assume a condition on the support of off-diagonal coefficients…
This paper has been withdrawn by the author due to a crucial error in the formulation.
In this paper we analyze some aspects of the "relativistic glider" proposed by Gu\'eron and Mosna more in detail. In particular an explicit weak gravity and low velocity expansion is presented, the influence of different initial conditions…
We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map…
We rigorously show that a local spin system giving rise to a slow Hamiltonian dynamics is stable against generic, even time-dependent, local perturbations. The sum of these perturbations can cover a significant amount of the system's size.…
In this note, we proved that weak limits, of sums of independent positive identically distributed random variables which are re-normalized by a non-linear shrinking transform $\max(0, x-r)$, are either degenerate or (some) compound Poisson…
We demonstrate a measure theoretical approach to the local regularity of weak supersolutions to elliptic and parabolic equations in divergence form. In the first part, we show that weak supersolutions become lower semicontinuous after…
This paper has been withdrawn by the authors due to an error in the proof of Lemma 3.9. The correct proof of global stability is given in arXiv:1101.5177
%auto-ignore This paper has been withdrawn by the authors.
This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.
A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way…
This paper has been withdrawn
This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.
In a 2013 paper, the author showed that the convolution of a compactly supported measure on the real line with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). In a 2014 paper, the author gave bounds for the optimal…
We establish two Phragm\'en--Lindel\"{o}f theorems for a fully nonlinear elliptic equation. We consider a dynamic boundary condition that includes both spatial variable and time derivative terms. As a spatial term, we consider a non-linear…