Benoît Kloeckner
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Registered User
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I am a teacher and researcher at Université Joseph Fourier.
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1d |
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Vector field pull back from embedding This is basic differential geometry, not research-level. I thought that Lev Soukhanov answer would show you where is the problem, but now the ongoing discussion does not belong here. Voting to close. |
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1d |
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Vector field pull back from embedding In other word, your "pull-back" vector field depends on both $f$ and $r$, while to properly define a $f^*X$ you would like it to depend only on $f$. |
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May 17 |
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Reference request: affine transforms + circle inversion? @Ryan Budney: the action of $\mathrm{PGL}$ does not contain the conformal group, as the former preserves the antipody relation while the latter doesn't. |
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May 14 |
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The pth power of a distance function is twice continuously differentiable, for $p>2$? Convexity is an assumption that may give you something, as stressed by Tom Bachmann below, connectivity is not. |
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May 14 |
awarded | ● Necromancer |
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May 13 |
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The Isoperimetric problem for domains constrained to lie between two parallel planes I took the liberty to improve your title and retag your question. |
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May 13 |
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The Isoperimetric problem for domains constrained to lie between two parallel planes changed the title and retaged |
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May 13 |
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integrals as duality pairing This is not the place to get a crash course on distributions or duality, and anyway you gave much too little information to get useful advice. |
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May 13 |
answered | chromatic number of the hyperbolic plane |
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May 10 |
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$\mathcal{D}(0,T;V)$ is dense in $W(0,T)$ What is $T$? What do the $0$s mean? What is $\mathcal{D}$? Is this question research-level? |
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May 10 |
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Vehicle Routing Problem with several constraints. You should explain a bit what the VRP is, or provide a link to definitions. |
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May 9 |
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Algebraic topology in low regularity @Ricardo Andrade: you are of course right, but one can take the trace - I edited the question accordingly. |
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May 9 |
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Algebraic topology in low regularity replaced restriction with trace and restricted to $s=1$ |
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May 9 |
asked | Algebraic topology in low regularity |
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May 9 |
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Homotopy equivalences preserving structure LaTexed the question |
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May 9 |
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Asymptotics of a function If one wants a crude asymptotic like the one Didier suggests, finding the dominant term for the lower bound and giving the obvious upper bound is sufficient. In any case, all ingredients are given in various comments, so either one cook up an answer that Granger will be able to accept, or we close as « off topic » (if the question is considered too simple) or « non longer relevant », but there is no need letting it popping up. |
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May 8 |
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Functional equations Your notation is a bit confusing when dealing with a functional equation, you should use indices $1$ and $2$ for the derivatives rather than variable names. |
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May 8 |
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Asymptotics of a function Didn't you took a $n$ for a $4$? The last term is $n^{-3n}$. |
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May 7 |
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Technical question on perimeter of level sets What kind of regularity do you have on $u$? |
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May 6 |
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Random rings linked into one component? @Ori Gurel-Gurevich: you are certainly right, I was too optimistic. I guess the method works under certain regularity assumptions (smooth or convex should work). |
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May 5 |
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the first eigenfunction of Dirichlet problem This is not a question suited for this site. |
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May 4 |
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Random graphs nonisomorphic to unit distance graphs I think you cannot exclude any given graph, because your random graphs are too sparse to exclude anything but forests. What you can try is to find an infinite family $\mathcal{F}$ of non-unit-distance finite graphs, and prove that as $n\to\infty$, your random graph will contain one of the members of $\mathcal{F}$ with high probability. This is probably a good exercise to someone wanting to get familiar with random groups. |
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May 4 |
accepted | Random graphs nonisomorphic to unit distance graphs |
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May 4 |
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Unbounded metrics on groups @Owen Sizemore: there is no compatibility with any given topology asked in the question. |
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May 4 |
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Diagonalize the simultaneous matrices and its background As far as I understand your question (which make little sense even after corrections: e.g. what is $F$ now?), it is basic material which you will find in any book treating these questions. Voting to close. |
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May 3 |
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Random graphs nonisomorphic to unit distance graphs I have thought a little bit about that, but I am not familiar enough with random graphs to answer. If I had the courage to make precise computations, I would bet on the family of wheels (one vertex connected to all vertices of a cycle) with more than 7 vertices, or more generally the family of graphs with one vertex connected to all the other, and the other inducing a graph with either a connected component of size $>6$ or a connected component with a vertex of degree 3. This makes a large family of non-unit-distance graphs, so it is somewhat likely that one of these graphs appears in $G$. |
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May 2 |
answered | Random graphs nonisomorphic to unit distance graphs |
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May 2 |
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Random graphs nonisomorphic to unit distance graphs It seems a bit harsh to me to close. I took the liberty to add precisions (which I hope do not depart from what the OP had in mind) that are better in the question than in comments; I think that there is question here, even if it is not very difficult once one has the right ingredients. |
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May 2 |
revised |
Random graphs nonisomorphic to unit distance graphs Gave precisions plus light edits |
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May 2 |
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Partition relation, almost a Ramsey cardinal? You shuold edit your question rather than post the edit as an answer! |
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May 2 |
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Positively curved manifold with a codimension 1 totally geodesic submanifold. Added a remark on localness |
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May 2 |
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Positively curved manifold with a codimension 1 totally geodesic submanifold. (...) I just remember that the problem is posed in a survey by Choe, Ritoré or both of them, but I could not get my hand on it. |
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May 2 |
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Positively curved manifold with a codimension 1 totally geodesic submanifold. @Ralph: no. As far as I know, very little has been written on this and the best lower bounds we have are the optimal linear bound (good for large domains) in complex dimension $2$ the Euclidean inequality (both for $\mathbb{CH}^n$) and optimal asymptotic bounds for small domains in all dimension (in a non-explicit sense). All are consequences of more general result (Yau's linear isoperimetric inequality, Croke's inequality for $4$-manifold with non-positive curvature, and Druet's inequality for manifolds with scalar curvature bounded above). |
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May 1 |
accepted | Random rings linked into one component? |
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May 1 |
accepted | Positively curved manifold with a codimension 1 totally geodesic submanifold. |
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Apr 30 |
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Positively curved manifold with a codimension 1 totally geodesic submanifold. added tags |
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Apr 30 |
answered | Positively curved manifold with a codimension 1 totally geodesic submanifold. |
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Apr 28 |
answered | Random rings linked into one component? |
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Apr 27 |
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Random rings linked into one component? (...) However, it seems that for any fixed circle, the probability that a random one is linked with it is bounded away from $0$, so there may be a clever coupling argument to use E-R random graphs. My guess is that the answer to all 3 questions is positive, except possibly Q3 when $S$ is lower-dimensional (in fact, a segment is my best bet to provide a negative example to Q3). |
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Apr 27 |
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Random rings linked into one component? I thought I had a simple answer, and then it turns out that your question is more interesting than my (incorrect) answer. My idea was to rephrase your connectedness question as follows: is the graph whose vertices are the circles and the edges are the pair of linked circles connected? Then, to use the Erdös-Renyi model for random graphs. With fixed parameter $p$ and $n\to\infty$, the connectedness probability goes to $1$. But the probability of connection between the circles are not independent, so we cannot apply the Erdös-Renyi model. (...) |
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Apr 26 |
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Riemannian manifolds with small geodesics and bounded curvature Why should $\gamma$ disconnect your surface? think of a torus, or a hyperbolic surface with small non-separating systole. |
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Apr 26 |
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weighted graph plot Note that the triangular inequality may be an obstruction to the construction of such a visualization, depending on the weights and the precise relation you want between weights and length. |
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Apr 23 |
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Reference for ultrametric spaces Thanks for the suggestion, but as I did my homework, I knew the existence of this paper; the point is that the correspondence itself is said to be "well-known" in the abstract, so this is not the primary reference for this particular point. Besides, its purpose is to describe categorically this correspondence, so there seems to be quite little about other structural properties of ultrametric spaces. This comment applies equally well to Lemin's paper cited by Peter Michor. |
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Apr 18 |
accepted | when constant scalar curvature implies Einstein? |
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Apr 17 |
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when constant scalar curvature implies Einstein? Umlauted Kähler. |
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Apr 17 |
answered | geometric interpretation of Lie bracket |
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Apr 17 |
accepted | Finding a good ordering of $\mathbb{Q}$ |
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Apr 17 |
answered | Finding a good ordering of $\mathbb{Q}$ |
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Apr 17 |
answered | when constant scalar curvature implies Einstein? |
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Apr 15 |
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Is there a lower bound for variance in terms of curvature? I guess I did not understand the question then. You are taking a domain of unit area with respect to $dx dy$, but you compute your integrals and variance according to the normalized volume of $g$? |
