# Benoît Kloeckner

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bio website www-fourier.ujf-grenoble.fr/… location Grenoble, France age 33 member for 3 years, 11 months seen 21 hours ago profile views 2,554
I am a teacher and researcher at UniversitÃ© Joseph Fourier.

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 2d comment Invertibility of NxN nonnegative matrix with diagonally dominant elements A Baire-generic matrix (without restriction on coefficients) is invertible, and your restriction consist in considering an open subset of all matrices. So sure the matrix you consider is generically invertible. I doubt you will find a reference as it is not specific to your particular restrictions at all. Mar6 revised Invariant subsets of $z \mapsto z^2$ changed the tag Mar4 reviewed Edit suggested edit on How is the Fractal Dimension of a Parametric Curve Related to the Fractal Dimensions of its Coordinate Functions? Mar4 revised How is the Fractal Dimension of a Parametric Curve Related to the Fractal Dimensions of its Coordinate Functions? missing par. Mar1 comment Triangle with largest perimeter in a convex region @JosephO'Rourke: the circle of radius $1/\sqrt{\pi}$ does. Mar1 comment Minimal piecewise-linear knot diagram I feel your question is not precise enough to get an interesting answer. Do you ask for an explicit algorithm, for complexity bounds, for NP-hardness? Mar1 reviewed Approve suggested edit on Limits of functions with converging zeros Feb28 comment quantitative version of the rigidity of the 2-sphere For the case of an embedded surface in $\mathbb{R}^3$, I would try to adapt the proof of the constant curvature case; more precisely, one can hope to prove that the Gauss map, which is a diffeomorphism since curvature is positive, is in fact close to be an isometry. Maybe the Hilbert argument (see e.g. Montiel-Ros page 92 and below) can be adapted to get that the principal curvatures must be uniformly close one to another. Feb28 comment quantitative version of the rigidity of the 2-sphere @Paul: you have to be careful how to define $|g_\Sigma- g_{S^2}|$, so as to identify different but isometric metrics. Feb27 comment Curvature for $C^{1,\alpha}$-metrics I do not see a proper reason to close it ("no longer relevant" is not an option anymore), so the best way to go could be for you to post your edit as an answer, possibly in a slightly more detailed form, and accept it. Feb26 comment Methods of probability theory in differential geometry fruitful? The question seems too vague to me, in fact I can hardly tell what the question is. Right now I cannot tell whether random walks on manifolds answer the question. Feb25 comment More than $n$ approximately orthonormal vectors in $R^n$ The tag "measure-concentration" is a good hint: in large dimension, two uniform random unit vectors are close to orthogonal with very high probability, so you get (exponentially) many pairwise almost orthogonal vectors by simply drawing them at random. Feb24 comment Reference request: embedding the hyperbolic triangulation in $\mathbb{R}^3$ Maybe you could precise a few points: how exactly is defined $T_d$? I guess the triangle are regular, and that the valence is the valence of vertices. More important, I guess that the "isometric" embedding you seek is combinatorially isometric but realized with flat triangle, is that right? And of course, you do not mean isometric for the extrinsic distance, but that might be better to say so explicitly. Feb22 comment Null sets visited infinitely often by trajectories of the shift dynamical system @JulianNewman: your example is of the same taste as Anthony Quas' one. "The event that you're at one particular point of the circle" means you fix $x\in\mathbb{S}^1$, (the "particular point") and then consider $A=\{\omega\in\Omega | \omega(0)=x\}$. It is very useful in probability to learn how to be able to translate between short sentences and full statements of this kind. Feb18 revised Characterization of discs added 379 characters in body Feb18 comment Characterization of discs @AlexandreEremenko: no need for smoothness here, the boundary is Lipschitz and therefore satisfies the fundamental theorem of analysis (no devil staircase here). Feb17 answered Characterization of discs Feb16 reviewed Approve suggested edit on Computational approach deciding whether a set of Wang Tile could tile the space up to some size Feb11 comment Projections on a manifold @Barrett: your question still needs clarification: if the $f^q$ functions can be chosen after the points $x_i$ are fixed, then the result is obvious as you can have $f^q|_{\{x_i\}_{i=1}^n}$ take whatever value you want. So, I guess that you ask for functions $f^q$ such that for all points $x_i$, etc. Is that so? Feb11 comment Banach-Mazur distance to complex $\ell^1$ of a space containing real $\ell^1$ Ok, I missed the word "complex" in your question, sorry.