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Kalai, Gil
The Double Cap Conjecture ★★
Author(s): Kalai
Conjecture The largest measure of a Lebesgue measurable subset of the unit sphere of
containing no pair of orthogonal vectors is attained by two open caps of geodesic radius
around the north and south poles.
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Keywords: combinatorial geometry; independent set; orthogonality; projective plane; sphere
Cube-Simplex conjecture ★★★
Author(s): Kalai
Conjecture For every positive integer
, there exists an integer
so that every polytope of dimension
has a
-dimensional face which is either a simplex or is combinatorially isomorphic to a
-dimensional cube.
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