# Benoît Kloeckner

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bio website www-fourier.ujf-grenoble.fr/… location Grenoble, France age 33 member for 4 years seen 20 hours ago profile views 2,655
I am a teacher and researcher at UniversitÃ© Joseph Fourier.

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 Apr12 comment Deterministic shifts There are a few strange points in your question, possibly misprints (e.g. in the conjugacy, I guess there is a $S_1$ and a $S_2$). With regard to question (1), why can't you use the same construction as in the previous §, taking $\Omega_2=\Omega_1^\mathbb{Z}$? Apr11 comment $C^\infty$ approximations of $f(r) = |r|^{m-1}r$ @riem: math.SE seems more suited to me than MO for your question. Your question about bounds on $f_n$ and $f'_n$ is odd: starting from an approximation $f_n$, you can set $g_n=f_{2^n}$ to improve any bound you had. Apr11 comment $C^\infty$ approximations of $f(r) = |r|^{m-1}r$ @PieroD'Ancona: this will not satisfy 4. (but by convexity one can then translate down the convolution to get 4.) Apr7 awarded Necromancer Apr7 comment An equivalence relation for norms Also, thinking about $\ell_p$'s one is tempted to say that if the group of linear mappings that preserves the strong equivalence class of a norm acts transitively on directions, then the norm should be strongly equivalent to $\ell_2$. Apr7 comment An equivalence relation for norms @alvarezpaiva: indeed I did not look at Willie's answer enough. I do not have any very precise idea; but you should probably kill the symmetry between $x$ and $y$ by writing them $z+v$ and $z-v$, thinking about $z$ as the direction you are looking at, and about $v$ as a perturbation of this direction. Most interesting things should happen when $v$ is relatively small. Apr7 comment An equivalence relation for norms As said by Suvrit, you are more or less (probably more than less) asking that the two norms have the same modulus of convexity "in each direction". In particular, no two $\ell_p$ norms are strongly equivalent. Apr6 comment Holomorphic maps on $\mathbb{R}^{n}$ (for n not necessarily even) Moreover conformal maps need not be holomorphic (even rotations can send a complex line to a totally real plane). Apr5 comment Locally flat submanifold Apr5 awarded mg.metric-geometry Apr1 comment curvature and volume growth Could you give some background, motivation, and things you tried? Mar31 awarded Necromancer Mar31 comment How many unit cylinders can touch a unit ball? @WlodekKuperberg: if the two triples of cylinders move symmetrically, then this movement is satisfying step 1. This does not imply that it cannot happen, but that the statement "step 1 => lockedness" would rule out such a movement. Mar31 awarded Revival Mar31 answered How many unit cylinders can touch a unit ball? Mar28 revised Furstenberg $\times 2 \times 3$ conjecture, bibliography Added a clarification in response to Asaf comment. Mar28 awarded Nice Answer Mar28 revised Low dimensional topological manifolds added 12 characters in body Mar27 answered Low dimensional topological manifolds Mar27 awarded Yearling