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 Yearling
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Mar
11
accepted Convex body with affine-equivalent cross-sections
Mar
11
comment Convex body with affine-equivalent cross-sections
Yes, as well as for the cylinder over any planar convex set. I was thinking about the strictly convex case. I can prove the local version for smooth strictly convex bodies and $k=2$.
Mar
11
comment Convex body with affine-equivalent cross-sections
Thanks! By chance, do you know anything about the local variant: if there is an open set of planes whose sections are equivalent, then these sections are ellipses?
Mar
11
comment Convex body with affine-equivalent cross-sections
@Deane: I mean that there are linear maps between 2-planes that send cross-sections one to another. The group of self-equivalences of a cross-section is indeed a subgroup of $SL(2,\mathbb R)$.
Mar
10
asked Convex body with affine-equivalent cross-sections
Mar
3
awarded  Yearling
Jan
12
comment A Converse to Cartan–Hadamard theorem?
Igor, a manifold without conjugate points can have some amount of positive Ricci curvature. There are 2-dimensional examples. The paper you cite claims that it should have negative Ricci curvature somewhere in a certain set.
Jan
12
reviewed Approve trace-formula tag wiki excerpt
Aug
19
awarded  Good Answer
Jul
17
awarded  Popular Question
Jun
24
comment An unfair marriage lemma
@Dominic van der Zypen: Yes we have just finished it. It is on arxiv.org/abs/1506.06781
Jun
24
awarded  Good Answer
Apr
29
comment An unfair marriage lemma
@David: Because we tested it on live analysts. It turns out that the very language of graph theory is not as widely understood as one might hope.
Apr
29
comment An unfair marriage lemma
@bof: I think we are going to thank you in acknowledgements. Do you prefer to be mentioned as an anonym or by some real name?
Apr
24
awarded  Popular Question
Apr
24
accepted An unfair marriage lemma
Apr
24
comment An unfair marriage lemma
Thanks! I tracked it from Mirski & Perfect's paper down to Dulmage & Mendelsohn, Coverings of bipartite graphs, Canad. J. Math. 10 (1958) 517-534, Theorem 1. And there (unlike the other sources) it is exactly it, not something that one has to combine with Hall's Theorem.
Apr
23
comment An unfair marriage lemma
Yes, we have the very same argument. It would be 5 lines long if we were aiming at combinatorialists. But it took more than a page to make the text consumable by analysts.
Apr
23
awarded  Nice Question
Apr
23
comment An unfair marriage lemma
@darij: Yes, of course we will prove it in the paper if there is no reference. It just looks too natural to be unknown.