6,634 reputation
2441
bio website www-fourier.ujf-grenoble.fr/…
location Grenoble, France
age 33
visits member for 4 years
seen 20 hours ago
I am a teacher and researcher at Université Joseph Fourier.

Apr
12
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 $\Omega_2=\Omega_1^\mathbb{Z}$?
Apr
11
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.
Apr
11
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.)
Apr
7
awarded  Necromancer
Apr
7
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 $\ell_2$.
Apr
7
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.
Apr
7
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.
Apr
6
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).
Apr
5
comment Locally flat submanifold
See mathoverflow.net/questions/58061/…
Apr
5
awarded  mg.metric-geometry
Apr
1
comment curvature and volume growth
Could you give some background, motivation, and things you tried?
Mar
31
awarded  Necromancer
Mar
31
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.
Mar
31
awarded  Revival
Mar
31
answered How many unit cylinders can touch a unit ball?
Mar
28
revised Furstenberg $\times 2 \times 3$ conjecture, bibliography
Added a clarification in response to Asaf comment.
Mar
28
awarded  Nice Answer
Mar
28
revised Low dimensional topological manifolds
added 12 characters in body
Mar
27
answered Low dimensional topological manifolds
Mar
27
awarded  Yearling