2,514 research outputs found
The Normal Form Theorem around Poisson Transversals
We prove a normal form theorem for Poisson structures around Poisson
transversals (also called cosymplectic submanifolds), which simultaneously
generalizes Weinstein's symplectic neighborhood theorem from symplectic
geometry and Weinstein's splitting theorem. Our approach turns out to be
essentially canonical, and as a byproduct, we obtain an equivariant version of
the latter theorem.Comment: 15 pages; v2: the title was changed; v3: proof of Lemma 2 was
include
Line transversals to disjoint balls
We prove that the set of directions of lines intersecting three disjoint
balls in in a given order is a strictly convex subset of . We then
generalize this result to disjoint balls in . As a consequence, we can
improve upon several old and new results on line transversals to disjoint balls
in arbitrary dimension, such as bounds on the number of connected components
and Helly-type theorems.Comment: 21 pages, includes figure
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